Fundamentos del análisis funcional

Este libro está dirigido principalmente a estudiantes de pregrado y se espera que el lector tenga conocimiento de la teoría de conjuntos, principalmente de cardinalidad y, además, de algunos tópicos relacionados con espacios métricos y análisis real.

Autores:
Aduén Muskus, Hugo
Herrón Osorio, Sigifredo
Tipo de recurso:
Book
Fecha de publicación:
2025
Institución:
Universidad de Córdoba
Repositorio:
Repositorio Institucional Unicórdoba
Idioma:
spa
OAI Identifier:
oai:repositorio.unicordoba.edu.co:ucordoba/9543
Acceso en línea:
https://repositorio.unicordoba.edu.co/handle/ucordoba/9543
https://repositorio.unicordoba.edu.co/
Palabra clave:
Análisis funcional
Análisis matemático
Rights
openAccess
License
Copyright Universidad de Córdoba, 2025
id UCORDOBA2_d1c2b869cda89dc9da708109cf218b3c
oai_identifier_str oai:repositorio.unicordoba.edu.co:ucordoba/9543
network_acronym_str UCORDOBA2
network_name_str Repositorio Institucional Unicórdoba
repository_id_str
dc.title.none.fl_str_mv Fundamentos del análisis funcional
title Fundamentos del análisis funcional
spellingShingle Fundamentos del análisis funcional
Análisis funcional
Análisis matemático
title_short Fundamentos del análisis funcional
title_full Fundamentos del análisis funcional
title_fullStr Fundamentos del análisis funcional
title_full_unstemmed Fundamentos del análisis funcional
title_sort Fundamentos del análisis funcional
dc.creator.fl_str_mv Aduén Muskus, Hugo
Herrón Osorio, Sigifredo
dc.contributor.author.none.fl_str_mv Aduén Muskus, Hugo
Herrón Osorio, Sigifredo
dc.subject.lcsh.spa.fl_str_mv Análisis funcional
Análisis matemático
topic Análisis funcional
Análisis matemático
description Este libro está dirigido principalmente a estudiantes de pregrado y se espera que el lector tenga conocimiento de la teoría de conjuntos, principalmente de cardinalidad y, además, de algunos tópicos relacionados con espacios métricos y análisis real.
publishDate 2025
dc.date.accessioned.none.fl_str_mv 2025-08-29T20:32:47Z
dc.date.available.none.fl_str_mv 2025-08-29T20:32:47Z
dc.date.issued.none.fl_str_mv 2025-08-29
dc.type.none.fl_str_mv Libro
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dc.identifier.instname.none.fl_str_mv Universidad de Córdoba
dc.identifier.reponame.none.fl_str_mv Repositorio Universidad de Córdoba
dc.identifier.repourl.none.fl_str_mv https://repositorio.unicordoba.edu.co/
dc.identifier.eisbn.none.fl_str_mv 978-628-7808-08-9
url https://repositorio.unicordoba.edu.co/handle/ucordoba/9543
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identifier_str_mv Universidad de Córdoba
Repositorio Universidad de Córdoba
978-628-7808-08-9
dc.language.iso.none.fl_str_mv spa
language spa
dc.relation.references.none.fl_str_mv [1] Hans Wilhelm Alt. Linear functional analysis. An application-oriented introduction. Translated from the 6th German edition by Robert Nürn- berg. London: Springer, 2016.
[2] Dan Amir. Characterizations of Inner Product Spaces. Operator Theory: Advances and Applications. Birkhäuser Basel, 2013.
[3] T. Apostol. Mathematical analysis. 2nd ed. Addison-Wesley Publishing Company, 1974.
[4] George Bachman and Lawrence Narici. Functional analysis. Reprint of the 1966 original. Mineola, NY: Dover Publications, reprint of the 1966 original edition, 2000.
[5] Sterling K. Berberian. Lectures in functional analysis and operator theory., volume 15. Springer, New York, NY, 1974.
[6] Rajendra Bhatia. Notes on functional analysis., volume 50. New Delhi: Hindustan Book Agency, 2009.
[7] Piotr Biler and Alfred Witkowski. Problems in mathematical analysis., volume 132. New York etc.: Marcel Dekker, Inc., 1990.
[8] Charles E. Blair. The Baire category theorem implies the principle of dependent choices. Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys., 25:933–934, 1977.
[9] R. Bonic. Linear functional analysis. Gordon and Breach Science Pu- blishers., 1969.
[10] Adam Bowers and Nigel J. Kalton. An introductory course in functional analysis. New York, NY: Springer, 2014.
[11] Alberto Bressan. Lecture notes on functional analysis. With applications to linear partial differential equations., volume 143. Providence, RI: American Mathematical Society (AMS), 2013.
[12] Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. New York, NY: Springer, 2011.
[13] A. Brown and A. Page. Elements of functional analysis. The New Uni- versity Mathematics Series. London etc.: Van Nostrand Reinhold Com- pany., 1970.
[14] Arlen Brown and Carl Pearcy. Introduction to operator theory. I. Ele- ments of functional analysis., volume 55. Springer, New York, NY, 1977.
[15] Victor Bryant. Reducing classical axioms. The Mathematical Gazette, 55(391):38–40, 1971.
[16] J. W. S. Cassels. Local fields, volume 3 of Lond. Math. Soc. Stud. Texts. Cambridge University Press, Cambridge, 1986.
[17] Joan Cerdà. Linear functional analysis., volume 116. Providence, RI: American Mathematical Society (AMS); Madrid: Real Sociedad Mate- mática Española, 2010.
[18] Gerardo R. Chacón, Humberto Rafeiro, and Juan Camilo Vallejo. Fun- ctional analysis. A terse introduction. Berlin: De Gruyter, 2017.
[19] Philippe G. Ciarlet. Linear and nonlinear functional analysis with ap- plications. With 401 problems and 52 figures., volume 130. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM)., 2013.
[20] John B. Conway. A course in functional analysis. 2nd ed., volume 96. New York etc.: Springer-Verlag, 2nd ed. edition, 1990.
[21] Constantin Costara and Dumitru Popa. Exercises in functional analysis. Dordrecht: Kluwer Academic Publishers, 2003.
[22] D. G. DeFigueiredo and L. A. Karlovitz. On the radial projection in normed spaces. Bull. Amer. Math. Soc., 73(3):364–368, 05 1967.
[23] F.R. Deutsch. Best Approximation in Inner Product Spaces. CMS Books in Mathematics. Springer New York, 2012.
[24] Jean Dieudonné. History of functional analysis., volume 49. Elsevier, Amsterdam, 1981.
[25] Jean Dieudonné. History of functional analysis. 1st reprint., volume 49. Elsevier, Amsterdam, 1983.
[26] R. Edwards. Functional analysis. Theory and applications. New York: Holt Rinehart and Winston., 1965.
[27] Yuli Eidelman, Vitali Milman, and Antonis Tsolomitis. Functional analy- sis. An introduction., volume 66. Providence, RI: American Mathema- tical Society (AMS), 2004.
[28] H. Enderton. Elements of set theory. New York: Academic Press, 1977.
[29] Otto Endler. Valuation theory. Universitext. Springer, Cham, 1972.
[30] Per Enflo. A counterexample to the approximation problem in Banach spaces. Acta Math., 130:309–317, 1973.
[31] R. Espinosa. Los matemáticos del café escocés. Laberintos e Infinitos, pages 26–30, Invierno 2003.
[32] Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos Santalu- cía, Jan Pelant, and Václav Zizler. Functional analysis and infinite- dimensional geometry., volume 8. New York, NY: Springer, 2001.
[33] Douglas Farenick. Fundamentals of functional analysis. Cham: Springer, 2016.
[34] Shaul R. Foguel. On a theorem by A. E. Taylor. Proc. Am. Math. Soc., 9:325, 1958.
[35] G. Gatica. Introducción al Análisis Funcional. Teoría y Aplicaciones. Reverte Ediciones S.A. de C.V., 2014.
[36] J.R. Giles. Introduction to the Analysis of Normed Linear Spaces. Australian Mathematical Society Lecture Series. Cambridge University Press, 2000.
[37] C. Goffman and G. Pedrick. First course in functional analysis. 2nd ed. New York: Chelsea Publishing Company., 1983.
[38] Dzung Minh Ha. Functional analysis. Vol. 1: A gentle introduction. Ithaca, NY: Matrix Editions, 2006.
[39] Markus Haase. Functional analysis. An elementary introduction., volume 156. Providence, RI: American Mathematical Society (AMS), 2014.
[40] Paul R. Halmos. A Hilbert space problem book. Reprint., volume 19. Springer, New York, NY, 1974.
[41] Vagn Lundsgaard Hansen. Functional analysis. Entering Hilbert space. Hackensack, NJ: World Scientific, 2006.
[42] Vagn Lundsgaard Hansen. Functional analysis. Entering Hilbert space. 2nd edition. Hackensack, NJ: World Scientific, 2nd edition edition, 2016.
[43] H. Hasse. Number theory. Transl. from the 3rd German. Class. Math. Berlin: Springer, reprint of the 1980 edition edition, 2002.
[44] A. Ya. Helemskii. Lectures and exercises on functional analysis., volume 233. Providence, RI: American Mathematical Society (AMS), 2006.
[45] H. Heuser. Functional analysis. Transl. by John Horvath. A Wiley- Interscience Publication. Chichester etc.: John Wiley & Sons., 1982.
[46] Francis Hirsch and Gilles Lacombe. Elements of functional analysis. Transl. from the French by Silvio Levy., volume 192. New York, NY: Springer, 1999.
[47] Vivian Hutson, John S. Pym, and Michael J. Cloud. Applications of fun- ctional analysis and operator theory. 2nd ed., volume 200. Amsterdam: Elsevier, 2nd ed. edition, 2005.
[48] P. K. Jain, O. P. Ahuja, and Khalil Ahmad. Functional analysis. New Delhi: New Age International (P) Ltd, Publishers (formerly Wiley Eas- tern Ltd), 1995.
[49] R. C. James. Characterizations of reflexivity. Stud. Math., 23:205–216, 1964.
[50] Robert C. James. A nonrelexive Banach space isometric with its second conjugate space. Proc. Natl. Acad. Sci. USA, 37:174–177, 1951.
[51] T.J. Jech. The Axiom of Choice. Dover Books on Mathematics. Dover Publications, 2013.
[52] P. Jorden and J. von Neumann. On inner products in linear, metric spaces. Ann. Math. (2), 36:719–723, 1935.
[53] Hugo D. Junghenn. Principles of analysis. Measure, integration, fun- ctional analysis, and applications. Boca Raton, FL: CRC Press, 2018.
[54] Vladimir Kadets. A course in functional analysis and measure theory. Translated from the Russian by Andrei Iacob. Cham: Springer, 2018.
[55] Shizuo Kakutani. Some characterizations of Euclidean space. Jpn. J. Math., 16:93–97, 1939.
[56] L. Kantorovich and G. P. Akilov. Functional analysis. Transl. from the Russian by Howard L. Silcock. 2nd ed. Oxford etc.: Pergamon Press., 1982.
[57] S. Kesavan. Topics in functional analysis and applications. New York etc.: John Wiley &| Sons, Inc.; New Delhi: Wiley Eastern Limited, 1989.
[58] S. Kesavan. Functional analysis., volume 52. New Delhi: Hindustan Book Agency, 2009.
[59] S. Kesavan. Functional analysis. Corrected reprint of the 2009 hard- back edition., volume 52. New Delhi: Hindustan Book Agency, corrected reprint of the 2009 hardback edition edition, 2014.
[60] A. A. Kirillov and A. D. Gvishiani. Theorems and problems in functional analysis. Transl. from the Russian by Harold H. McFaden. Springer, Cham, 1982.
[61] Vilmos Komornik. Lectures on functional analysis and the Lebesgue integral. Translated from the French by the author. London: Springer, 2016.
[62] Erwin Kreyszig. Introductory functional analysis with applications. New York etc.: John Wiley & Sons., 1978.
[63] V. K. Krishnan. Textbook of functional analysis. A problem-oriented approach. 2nd edition. New Delhi: PHI Learning, 2nd edition edition, 2014.
[64] C.S. Kubrusly. The Elements of Operator Theory. Birkhäuser Boston, 2011.
[65] Marek Kuczma. An introduction to the theory of functional equations and inequalities. Cauchy’s equation and Jensen’s inequality. Edited by Attila Gilányi. 2nd ed. Basel: Birkhäuser, 2nd ed. edition, 2009.
[66] A. Kumar, S. Kumaresan, and B.K. Sarma. A Foundation Course in Mathematics. Alpha Science International, 2017.
[67] S. Kumaresan. Topology of Metric Spaces. Alpha Science International, 2005.
[68] S. S. Kutateladze. Fundamentals of functional analysis. Transl. from the Russian. Dordrecht: Kluwer Academic Publishers, 1995.
[69] Serge Lang. Real and functional analysis. 3. ed., volume 142. New York: Springer-Verlag, 3. ed. edition, 1993.
[70] Peter D. Lax. Functional analysis. Chichester: Wiley, 2002.
[71] B. Limaye. Functional analysis. 2nd ed. New Delhi: New Age Interna- tional Limited, 1996.
[72] B. Limaye. Linear functional analysis for scientists and engineers. Sin- gapore: Springer, 2016.
[73] J. Lindenstrauss and L. Tzafriri. On the complemented subspaces pro- blem. Isr. J. Math., 9:263–269, 1971.
[74] L. Lusternik and V. Sobolev. Elements of functional analysis. Authori- sed 3rd English translation from 2nd extensively enlarged and rewritten Russian edition. A Halsted Press Book. Delhi: Hindustan Publishing Corpn.; New York: John Wiley & Sons, Inc., 1974.
[75] Barbara D. MacCluer. Elementary functional analysis., volume 253. New York, NY: Springer, 2009.
[76] D. Mauldin. The Scottish Book. Mathematics from the Scottish Cafe. Boston - Basel - Stuttgart: Birkhäuser. XIII, 268 p. DM 58.00 (1981)., 1981.
[77] Reinhold Meise and Dietmar Vogt. Introduction to functional analysis. Transl. from the German by M. S. Ramanujan., volume 2. Oxford: Clarendon Press, 1997.
[78] A. F. Monna. Functional analysis in historical perspective. Academische Paperbacks. Utrecht, The Netherlands: Oosthoek , 1973.
[79] Terry J. Morrison. Functional analysis. An introduction to Banach space theory. Chichester: Wiley, 2001.
[80] A. Mukherjea and K. Pothoven. Real and functional analysis. 2nd ed. Part A: Real analysis. Mathematical concepts and methods in Science and Engineering, 27. New York, 1984.
[81] A. Mukherjea and K. Pothoven. Real and functional analysis. 2nd ed. Part B: Functional analysis. Mathematical Concepts and Methods in Science and Engineering, 28. New York, 1986.
[82] Joseph Muscat. Functional analysis. An introduction to metric spaces, Hilbert spaces, and Banach algebras. Cham: Springer, 2014.
[83] M. Thamban Nair. Functional analysis. A first course. New Delhi: Prentice-Hall of India, 2002.
[84] Ivan Niven. Irrational numbers., volume 11. Mathematical Association of America, Washington, DC, 1956.
[85] J. Tinsley Oden and Leszek F. Demkowicz. Applied functional analysis. 2nd ed. Boca Raton, FL: CRC Press, 2nd ed. edition, 2010.
[86] Sergei Ovchinnikov. Functional analysis. An introductory course. Cham: Springer, 2018.
[87] A. Pietsch. History of Banach Spaces and Linear Operators. Birkhäuser Boston, 2007.
[88] S. Ponnusamy, editor. Foundations of functional analysis. Pangbourne: Alpha Science International; Boca Raton, FL: CRC Press, 2002.
[88] S. Ponnusamy, editor. Foundations of functional analysis. Pangbourne: Alpha Science International; Boca Raton, FL: CRC Press, 2002.
[90] Matthew A. Pons. Real analysis for the undergraduate. With an invita- tion to functional analysis. New York, NY: Springer, 2014.
[91] S. David Promislow. A first course in functional analysis. Hoboken, NJ: John Wiley & Sons, 2008.
[92] Frigyes Riesz and Béla Sz.-Nagy. Functional analysis. Transl. from the 2nd French ed. by Leo F. Boron. Reprint of the 1955 orig. publ. by Ungar Publ. Co. New York: Dover Publications, Inc., reprint of the 1955 orig. publ. by ungar publ. co. edition, 1990.
[93] W. Rudin. Principles of Mathematical Analysis. International series in pure and applied mathematics. McGraw-Hill, 1976.
[94] W. Rudin. Real and Complex Analysis. McGraw-Hill series in higher mathematics. Tata McGraw-Hill, 2006.
[95] Walter Rudin. Functional analysis. 2nd ed. New York, NY: McGraw- Hill, 2nd ed. edition, 1991.
[96] Bryan P. Rynne and Martin A. Youngson. Linear functional analysis. London: Springer, 2000.
[97] Bryan P. Rynne and Martin A. Youngson. Linear functional analysis. 2nd ed. London: Springer, 2nd ed. edition, 2008.
[98] Amol Sasane. A friendly approach to functional analysis. Hackensack, NJ: World Scientific, 2017.
[99] Karen Saxe. Beginning functional analysis. New York, NY: Springer, 2002.
[100] M. Schechter. Principles of functional analysis. New York-London: Academic Press, 1971.
[101] Martin Schechter. Principles of functional analysis. 2nd ed., volume 36. Providence, RI: American Mathematical Society (AMS), 2nd ed. edition, 2001.
[102] Peter Schneider. Nonarchimedean functional analysis. Springer Monogr. Math. Berlin: Springer, 2002.
[103] Rabindranath Sen. A first course in functional analysis. Theory and applications. London: Anthem Press, 2013.
[104] Orr Moshe Shalit. A first course in functional analysis. Boca Raton, FL: CRC Press, 2017.
[105] Abul Hasan Siddiqi. Functional analysis and applications. Singapore: Springer, 2018.
[106] Alan D. Sokal. A really simple elementary proof of the uniform boun- dedness theorem. Am. Math. Mon., 118(5):450–452, 2011.
[107] Elias M. Stein and Rami Shakarchi. Functional analysis. Introduction to further topics in analysis. Princeton, NJ: Princeton University Press, 2011.
[108] Erdoğan S. Şuhubi. Functional analysis. Dordrecht: Kluwer Academic Publishers, 2003.
[109] V. S. Sunder. Functional analysis: spectral theory., volume 13. New Delhi: Hindustan Book Agency, 1997.
[110] Charles Swartz. An introduction to functional analysis., volume 157. New York etc.: Marcel Dekker, 1992.
[111] Charles Swartz. Elementary functional analysis. Hackensack, NJ: World Scientific, 2009.
[112] A. Taylor and D. Lay. Introduction to functional analysis. 2nd ed. (Re- print of the orig. 1980, publ. by John Wiley & Sons, Inc., New York etc.). Malabar, Florida: Robert E. Krieger Publishing Company. XI, 467 p., 1986.
[113] Alberto Torchinsky. Problems in real and functional analysis., volume 166. Providence, RI: American Mathematical Society (AMS), 2015.
[114] V. Trénoguine. Analyse fonctionnelle. Traduit du Russe: Mathéma- tiques. [Translations of Russian Works: Mathematics]. “Mir”, Moscow, 1985. Translated from the Russian by V. Kotliar.
[115] A. C. M. van Rooij. Non-Archimedean functional analysis, volume 51 of Pure Appl. Math., Marcel Dekker. Marcel Dekker, Inc., New York, NY, 1978.
[116] B. Z. Vulikh. Introduction to functional analysis for scientists and tech- nologists. International Series of Monographs on Pure and Applied Mathematics. 32. Oxford etc.: Pergamon Press, 1963.
[117] William R. Wade. An introduction to analysis. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 2nd ed. edition, 2000.
[118] J. F. Rigby; James Wiegold. Independent axioms for vector spaces. The Mathematical Gazette, 57(399):56–62, 1973.
[119] A. Wilansky. Functional analysis. New York-Toronto-London: Blaisdell Publishing Company, a division of Ginn and Company, 1964.
[120] Albert Wilansky. The bounded additive operation on Banach space. Proc. Am. Math. Soc., 2:46, 1951.
[121] Michel Willem. Functional analysis. Fundamentals and applications. New York, NY: Birkhäuser/Springer, 2013.
[122] Yutaka Yamamoto. From vector spaces to function spaces. Introduction to functional analysis with applications., volume 127. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), 2012.
[123] K. Yosida. Functional analysis. Berlin-Göttingen-Heidelberg: Springer- Verlag, 1965.
[124] Kosaku Yosida. Functional analysis. Repr. of the 6th ed. Berlin: Springer-Verlag, repr. of the 6th ed. edition, 1994.
[125] Robert J. Zimmer. Essential results of functional analysis. Chicago etc.: The University of Chicago Press, 1990.
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spelling Aduén Muskus, HugoHerrón Osorio, Sigifredo2025-08-29T20:32:47Z2025-08-29T20:32:47Z2025-08-29https://repositorio.unicordoba.edu.co/handle/ucordoba/9543Universidad de CórdobaRepositorio Universidad de Córdobahttps://repositorio.unicordoba.edu.co/978-628-7808-08-9Este libro está dirigido principalmente a estudiantes de pregrado y se espera que el lector tenga conocimiento de la teoría de conjuntos, principalmente de cardinalidad y, además, de algunos tópicos relacionados con espacios métricos y análisis real.Introducción............ iv1. Espacios vectoriales 11.1. Definición de campo y valuaciones . . . . . . . . . . . . . . . . 11.2. Definición de espacio vectorial y ejemplos . . . . . . . . . . . . 91.3. Bases de Hamel y dimensión . . . . . . . . . . . . . . . . . . . . 271.4. Operadores Lineales . . . . . . . . . . . . . . . . . . . . . . . . 471.5. Funcionales lineales . . . . . . . . . . . . . . . . . . . . . . . . . 591.6. El teorema de Hahn-Banach en espacios lineales . . . . . . . . . 672. Espacios normados 822.1. Definiciones y ejemplos . . . . . . . . . . . . . . . . . . . . . . . 822.2. Espacios de Banach y ejemplos . . . . . . . . . . . . . . . . . . 912.3. Completación de un espacio normado . . . . . . . . . . . . . . . 1142.4. Espacios normados de dimensión finita . . . . . . . . . . . . . . 1182.5. El Teorema de Baire . . . . . . . . . . . . . . . . . . . . . . . . 1302.6. Bases de Schauder y separabilidad . . . . . . . . . . . . . . . . 1373. Operadores lineales acotados 1473.1. Definiciones, propiedades y ejemplos . . . . . . . . . . . . . . . 1473.2. Operadores invertibles . . . . . . . . . . . . . . . . . . . . . . . 1623.3. Funcionales lineales acotados . . . . . . . . . . . . . . . . . . . 1663.4. El teorema de Hahn-Banach en espacios normados . . . . . . . 1863.5. Dualidad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1993.6. Espacios reflexivos . . . . . . . . . . . . . . . . . . . . . . . . . 2133.7. El operador adjunto . . . . . . . . . . . . . . . . . . . . . . . . 2204. Teoremas fundamentales 2244.1. Teorema de Banach–Steinhaus . . . . . . . . . . . . . . . . . . 2254.2. Teorema de la aplicación abierta . . . . . . . . . . . . . . . . . 2324.3. Teorema de la gráfica cerrada . . . . . . . . . . . . . . . . . . . 2384.4. Teorema de normas equivalentes implica TBS . . . . . . . . . . 2475. Espacios de Hilbert 2505.1. Espacios prehilbertiano y espacios de Hilbert . . . . . . . . . . 2515.2. Ortogonalidad . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2645.3. Teorema de la distancia mínima . . . . . . . . . . . . . . . . . . 2705.4. Teorema de representación de Riesz . . . . . . . . . . . . . . . 2805.5. Sumas no ordenadas . . . . . . . . . . . . . . . . . . . . . . . . 2885.6. Conjuntos Ortonormales Completos . . . . . . . . . . . . . . . 2995.7. Adjunto de operador lineal acotado en un Hilbert . . . . . . . . 3035.8. Operadores autoadjunto, unitario y normal . . . . . . . . . . . 308Bibliografía....... 314Índice alfabético........... 323Primera ediciónapplication/pdfspaFondo Editorial - Universidad de CórdobaMontería, Córdoba, ColombiaCopyright Universidad de Córdoba, 2025https://creativecommons.org/licenses/by-nc-nd/4.0/Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Análisis funcionalAnálisis matemáticoFundamentos del análisis funcionalLibroinfo:eu-repo/semantics/bookhttp://purl.org/coar/resource_type/c_2f33info:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/LIB[1] Hans Wilhelm Alt. Linear functional analysis. An application-oriented introduction. Translated from the 6th German edition by Robert Nürn- berg. London: Springer, 2016.[2] Dan Amir. Characterizations of Inner Product Spaces. Operator Theory: Advances and Applications. Birkhäuser Basel, 2013.[3] T. Apostol. Mathematical analysis. 2nd ed. Addison-Wesley Publishing Company, 1974.[4] George Bachman and Lawrence Narici. Functional analysis. Reprint of the 1966 original. Mineola, NY: Dover Publications, reprint of the 1966 original edition, 2000.[5] Sterling K. Berberian. Lectures in functional analysis and operator theory., volume 15. Springer, New York, NY, 1974.[6] Rajendra Bhatia. Notes on functional analysis., volume 50. New Delhi: Hindustan Book Agency, 2009.[7] Piotr Biler and Alfred Witkowski. Problems in mathematical analysis., volume 132. New York etc.: Marcel Dekker, Inc., 1990.[8] Charles E. Blair. The Baire category theorem implies the principle of dependent choices. Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys., 25:933–934, 1977.[9] R. Bonic. Linear functional analysis. Gordon and Breach Science Pu- blishers., 1969.[10] Adam Bowers and Nigel J. Kalton. An introductory course in functional analysis. New York, NY: Springer, 2014.[11] Alberto Bressan. Lecture notes on functional analysis. With applications to linear partial differential equations., volume 143. Providence, RI: American Mathematical Society (AMS), 2013.[12] Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. New York, NY: Springer, 2011.[13] A. Brown and A. Page. Elements of functional analysis. The New Uni- versity Mathematics Series. London etc.: Van Nostrand Reinhold Com- pany., 1970.[14] Arlen Brown and Carl Pearcy. Introduction to operator theory. I. Ele- ments of functional analysis., volume 55. Springer, New York, NY, 1977.[15] Victor Bryant. Reducing classical axioms. The Mathematical Gazette, 55(391):38–40, 1971.[16] J. W. S. Cassels. Local fields, volume 3 of Lond. Math. Soc. Stud. Texts. Cambridge University Press, Cambridge, 1986.[17] Joan Cerdà. Linear functional analysis., volume 116. Providence, RI: American Mathematical Society (AMS); Madrid: Real Sociedad Mate- mática Española, 2010.[18] Gerardo R. Chacón, Humberto Rafeiro, and Juan Camilo Vallejo. Fun- ctional analysis. A terse introduction. Berlin: De Gruyter, 2017.[19] Philippe G. Ciarlet. Linear and nonlinear functional analysis with ap- plications. With 401 problems and 52 figures., volume 130. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM)., 2013.[20] John B. Conway. A course in functional analysis. 2nd ed., volume 96. New York etc.: Springer-Verlag, 2nd ed. edition, 1990.[21] Constantin Costara and Dumitru Popa. Exercises in functional analysis. Dordrecht: Kluwer Academic Publishers, 2003.[22] D. G. DeFigueiredo and L. A. Karlovitz. On the radial projection in normed spaces. Bull. Amer. Math. Soc., 73(3):364–368, 05 1967.[23] F.R. Deutsch. Best Approximation in Inner Product Spaces. CMS Books in Mathematics. Springer New York, 2012.[24] Jean Dieudonné. History of functional analysis., volume 49. Elsevier, Amsterdam, 1981.[25] Jean Dieudonné. History of functional analysis. 1st reprint., volume 49. Elsevier, Amsterdam, 1983.[26] R. Edwards. Functional analysis. Theory and applications. New York: Holt Rinehart and Winston., 1965.[27] Yuli Eidelman, Vitali Milman, and Antonis Tsolomitis. Functional analy- sis. An introduction., volume 66. Providence, RI: American Mathema- tical Society (AMS), 2004.[28] H. Enderton. Elements of set theory. New York: Academic Press, 1977.[29] Otto Endler. Valuation theory. Universitext. Springer, Cham, 1972.[30] Per Enflo. A counterexample to the approximation problem in Banach spaces. Acta Math., 130:309–317, 1973.[31] R. Espinosa. Los matemáticos del café escocés. Laberintos e Infinitos, pages 26–30, Invierno 2003.[32] Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos Santalu- cía, Jan Pelant, and Václav Zizler. Functional analysis and infinite- dimensional geometry., volume 8. New York, NY: Springer, 2001.[33] Douglas Farenick. Fundamentals of functional analysis. Cham: Springer, 2016.[34] Shaul R. Foguel. On a theorem by A. E. Taylor. Proc. Am. Math. Soc., 9:325, 1958.[35] G. Gatica. Introducción al Análisis Funcional. Teoría y Aplicaciones. Reverte Ediciones S.A. de C.V., 2014.[36] J.R. Giles. Introduction to the Analysis of Normed Linear Spaces. Australian Mathematical Society Lecture Series. Cambridge University Press, 2000.[37] C. Goffman and G. Pedrick. First course in functional analysis. 2nd ed. New York: Chelsea Publishing Company., 1983.[38] Dzung Minh Ha. Functional analysis. Vol. 1: A gentle introduction. Ithaca, NY: Matrix Editions, 2006.[39] Markus Haase. Functional analysis. An elementary introduction., volume 156. Providence, RI: American Mathematical Society (AMS), 2014.[40] Paul R. Halmos. A Hilbert space problem book. Reprint., volume 19. Springer, New York, NY, 1974.[41] Vagn Lundsgaard Hansen. Functional analysis. Entering Hilbert space. Hackensack, NJ: World Scientific, 2006.[42] Vagn Lundsgaard Hansen. Functional analysis. Entering Hilbert space. 2nd edition. Hackensack, NJ: World Scientific, 2nd edition edition, 2016.[43] H. Hasse. Number theory. Transl. from the 3rd German. Class. Math. Berlin: Springer, reprint of the 1980 edition edition, 2002.[44] A. Ya. Helemskii. Lectures and exercises on functional analysis., volume 233. Providence, RI: American Mathematical Society (AMS), 2006.[45] H. Heuser. Functional analysis. Transl. by John Horvath. A Wiley- Interscience Publication. Chichester etc.: John Wiley & Sons., 1982.[46] Francis Hirsch and Gilles Lacombe. Elements of functional analysis. Transl. from the French by Silvio Levy., volume 192. New York, NY: Springer, 1999.[47] Vivian Hutson, John S. Pym, and Michael J. Cloud. Applications of fun- ctional analysis and operator theory. 2nd ed., volume 200. Amsterdam: Elsevier, 2nd ed. edition, 2005.[48] P. K. Jain, O. P. Ahuja, and Khalil Ahmad. Functional analysis. New Delhi: New Age International (P) Ltd, Publishers (formerly Wiley Eas- tern Ltd), 1995.[49] R. C. James. Characterizations of reflexivity. Stud. Math., 23:205–216, 1964.[50] Robert C. James. A nonrelexive Banach space isometric with its second conjugate space. Proc. Natl. Acad. Sci. USA, 37:174–177, 1951.[51] T.J. Jech. The Axiom of Choice. Dover Books on Mathematics. Dover Publications, 2013.[52] P. Jorden and J. von Neumann. On inner products in linear, metric spaces. Ann. Math. (2), 36:719–723, 1935.[53] Hugo D. Junghenn. Principles of analysis. Measure, integration, fun- ctional analysis, and applications. Boca Raton, FL: CRC Press, 2018.[54] Vladimir Kadets. A course in functional analysis and measure theory. Translated from the Russian by Andrei Iacob. Cham: Springer, 2018.[55] Shizuo Kakutani. Some characterizations of Euclidean space. Jpn. J. Math., 16:93–97, 1939.[56] L. Kantorovich and G. P. Akilov. Functional analysis. Transl. from the Russian by Howard L. Silcock. 2nd ed. Oxford etc.: Pergamon Press., 1982.[57] S. Kesavan. Topics in functional analysis and applications. New York etc.: John Wiley &| Sons, Inc.; New Delhi: Wiley Eastern Limited, 1989.[58] S. Kesavan. Functional analysis., volume 52. New Delhi: Hindustan Book Agency, 2009.[59] S. Kesavan. Functional analysis. Corrected reprint of the 2009 hard- back edition., volume 52. New Delhi: Hindustan Book Agency, corrected reprint of the 2009 hardback edition edition, 2014.[60] A. A. Kirillov and A. D. Gvishiani. Theorems and problems in functional analysis. Transl. from the Russian by Harold H. McFaden. Springer, Cham, 1982.[61] Vilmos Komornik. Lectures on functional analysis and the Lebesgue integral. Translated from the French by the author. London: Springer, 2016.[62] Erwin Kreyszig. Introductory functional analysis with applications. New York etc.: John Wiley & Sons., 1978.[63] V. K. Krishnan. Textbook of functional analysis. A problem-oriented approach. 2nd edition. New Delhi: PHI Learning, 2nd edition edition, 2014.[64] C.S. Kubrusly. The Elements of Operator Theory. Birkhäuser Boston, 2011.[65] Marek Kuczma. An introduction to the theory of functional equations and inequalities. Cauchy’s equation and Jensen’s inequality. Edited by Attila Gilányi. 2nd ed. Basel: Birkhäuser, 2nd ed. edition, 2009.[66] A. Kumar, S. Kumaresan, and B.K. Sarma. A Foundation Course in Mathematics. Alpha Science International, 2017.[67] S. Kumaresan. Topology of Metric Spaces. Alpha Science International, 2005.[68] S. S. Kutateladze. Fundamentals of functional analysis. Transl. from the Russian. Dordrecht: Kluwer Academic Publishers, 1995.[69] Serge Lang. Real and functional analysis. 3. ed., volume 142. New York: Springer-Verlag, 3. ed. edition, 1993.[70] Peter D. Lax. Functional analysis. Chichester: Wiley, 2002.[71] B. Limaye. Functional analysis. 2nd ed. New Delhi: New Age Interna- tional Limited, 1996.[72] B. Limaye. Linear functional analysis for scientists and engineers. Sin- gapore: Springer, 2016.[73] J. Lindenstrauss and L. Tzafriri. On the complemented subspaces pro- blem. Isr. J. Math., 9:263–269, 1971.[74] L. Lusternik and V. Sobolev. Elements of functional analysis. Authori- sed 3rd English translation from 2nd extensively enlarged and rewritten Russian edition. A Halsted Press Book. Delhi: Hindustan Publishing Corpn.; New York: John Wiley & Sons, Inc., 1974.[75] Barbara D. MacCluer. Elementary functional analysis., volume 253. New York, NY: Springer, 2009.[76] D. Mauldin. The Scottish Book. Mathematics from the Scottish Cafe. Boston - Basel - Stuttgart: Birkhäuser. XIII, 268 p. DM 58.00 (1981)., 1981.[77] Reinhold Meise and Dietmar Vogt. Introduction to functional analysis. Transl. from the German by M. S. Ramanujan., volume 2. Oxford: Clarendon Press, 1997.[78] A. F. Monna. Functional analysis in historical perspective. Academische Paperbacks. Utrecht, The Netherlands: Oosthoek , 1973.[79] Terry J. Morrison. Functional analysis. An introduction to Banach space theory. Chichester: Wiley, 2001.[80] A. Mukherjea and K. Pothoven. Real and functional analysis. 2nd ed. Part A: Real analysis. Mathematical concepts and methods in Science and Engineering, 27. New York, 1984.[81] A. Mukherjea and K. Pothoven. Real and functional analysis. 2nd ed. Part B: Functional analysis. Mathematical Concepts and Methods in Science and Engineering, 28. New York, 1986.[82] Joseph Muscat. Functional analysis. An introduction to metric spaces, Hilbert spaces, and Banach algebras. Cham: Springer, 2014.[83] M. Thamban Nair. Functional analysis. A first course. New Delhi: Prentice-Hall of India, 2002.[84] Ivan Niven. Irrational numbers., volume 11. Mathematical Association of America, Washington, DC, 1956.[85] J. Tinsley Oden and Leszek F. Demkowicz. Applied functional analysis. 2nd ed. Boca Raton, FL: CRC Press, 2nd ed. edition, 2010.[86] Sergei Ovchinnikov. Functional analysis. An introductory course. Cham: Springer, 2018.[87] A. Pietsch. History of Banach Spaces and Linear Operators. Birkhäuser Boston, 2007.[88] S. Ponnusamy, editor. Foundations of functional analysis. Pangbourne: Alpha Science International; Boca Raton, FL: CRC Press, 2002.[88] S. Ponnusamy, editor. Foundations of functional analysis. Pangbourne: Alpha Science International; Boca Raton, FL: CRC Press, 2002.[90] Matthew A. Pons. Real analysis for the undergraduate. With an invita- tion to functional analysis. New York, NY: Springer, 2014.[91] S. David Promislow. A first course in functional analysis. Hoboken, NJ: John Wiley & Sons, 2008.[92] Frigyes Riesz and Béla Sz.-Nagy. Functional analysis. Transl. from the 2nd French ed. by Leo F. Boron. Reprint of the 1955 orig. publ. by Ungar Publ. Co. New York: Dover Publications, Inc., reprint of the 1955 orig. publ. by ungar publ. co. edition, 1990.[93] W. Rudin. Principles of Mathematical Analysis. International series in pure and applied mathematics. McGraw-Hill, 1976.[94] W. Rudin. Real and Complex Analysis. McGraw-Hill series in higher mathematics. Tata McGraw-Hill, 2006.[95] Walter Rudin. Functional analysis. 2nd ed. New York, NY: McGraw- Hill, 2nd ed. edition, 1991.[96] Bryan P. Rynne and Martin A. Youngson. Linear functional analysis. London: Springer, 2000.[97] Bryan P. Rynne and Martin A. Youngson. Linear functional analysis. 2nd ed. London: Springer, 2nd ed. edition, 2008.[98] Amol Sasane. A friendly approach to functional analysis. Hackensack, NJ: World Scientific, 2017.[99] Karen Saxe. Beginning functional analysis. New York, NY: Springer, 2002.[100] M. Schechter. Principles of functional analysis. New York-London: Academic Press, 1971.[101] Martin Schechter. Principles of functional analysis. 2nd ed., volume 36. Providence, RI: American Mathematical Society (AMS), 2nd ed. edition, 2001.[102] Peter Schneider. Nonarchimedean functional analysis. Springer Monogr. Math. Berlin: Springer, 2002.[103] Rabindranath Sen. A first course in functional analysis. Theory and applications. London: Anthem Press, 2013.[104] Orr Moshe Shalit. A first course in functional analysis. Boca Raton, FL: CRC Press, 2017.[105] Abul Hasan Siddiqi. Functional analysis and applications. Singapore: Springer, 2018.[106] Alan D. Sokal. A really simple elementary proof of the uniform boun- dedness theorem. Am. Math. Mon., 118(5):450–452, 2011.[107] Elias M. Stein and Rami Shakarchi. Functional analysis. Introduction to further topics in analysis. Princeton, NJ: Princeton University Press, 2011.[108] Erdoğan S. Şuhubi. Functional analysis. Dordrecht: Kluwer Academic Publishers, 2003.[109] V. S. Sunder. Functional analysis: spectral theory., volume 13. New Delhi: Hindustan Book Agency, 1997.[110] Charles Swartz. An introduction to functional analysis., volume 157. New York etc.: Marcel Dekker, 1992.[111] Charles Swartz. Elementary functional analysis. Hackensack, NJ: World Scientific, 2009.[112] A. Taylor and D. Lay. Introduction to functional analysis. 2nd ed. (Re- print of the orig. 1980, publ. by John Wiley & Sons, Inc., New York etc.). Malabar, Florida: Robert E. Krieger Publishing Company. XI, 467 p., 1986.[113] Alberto Torchinsky. Problems in real and functional analysis., volume 166. Providence, RI: American Mathematical Society (AMS), 2015.[114] V. Trénoguine. Analyse fonctionnelle. Traduit du Russe: Mathéma- tiques. [Translations of Russian Works: Mathematics]. “Mir”, Moscow, 1985. Translated from the Russian by V. Kotliar.[115] A. C. M. van Rooij. Non-Archimedean functional analysis, volume 51 of Pure Appl. Math., Marcel Dekker. Marcel Dekker, Inc., New York, NY, 1978.[116] B. Z. Vulikh. Introduction to functional analysis for scientists and tech- nologists. International Series of Monographs on Pure and Applied Mathematics. 32. Oxford etc.: Pergamon Press, 1963.[117] William R. Wade. An introduction to analysis. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 2nd ed. edition, 2000.[118] J. F. Rigby; James Wiegold. Independent axioms for vector spaces. The Mathematical Gazette, 57(399):56–62, 1973.[119] A. Wilansky. Functional analysis. New York-Toronto-London: Blaisdell Publishing Company, a division of Ginn and Company, 1964.[120] Albert Wilansky. The bounded additive operation on Banach space. Proc. Am. Math. Soc., 2:46, 1951.[121] Michel Willem. Functional analysis. Fundamentals and applications. New York, NY: Birkhäuser/Springer, 2013.[122] Yutaka Yamamoto. From vector spaces to function spaces. Introduction to functional analysis with applications., volume 127. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), 2012.[123] K. Yosida. Functional analysis. Berlin-Göttingen-Heidelberg: Springer- Verlag, 1965.[124] Kosaku Yosida. Functional analysis. Repr. of the 6th ed. Berlin: Springer-Verlag, repr. of the 6th ed. edition, 1994.[125] Robert J. Zimmer. Essential results of functional analysis. 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