A Note On Preservation Of Spectra For Two Given Operators
We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra c...
- Autores:
-
Carpintero, Carlos
Gutiérrez, Alexander
Rosas, Ennis
Sanabria, José
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2020
- Institución:
- Corporación Universitaria del Caribe - CECAR
- Repositorio:
- Repositorio Digital CECAR
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.cecar.edu.co:cecar/10907
- Acceso en línea:
- https://repositorio.cecar.edu.co/handle/cecar/10907
- Palabra clave:
- Restriction of an operator
Spectral property
Semi-Fredholm spectra
Multiplication operator
- Rights
- openAccess
- License
- Derechos Reservados. Corporación Universitaria del Caribe – CECAR
| id |
RepoCECAR2_0094bbf76801aae1bd7ff49bd11a6b49 |
|---|---|
| oai_identifier_str |
oai:repositorio.cecar.edu.co:cecar/10907 |
| network_acronym_str |
RepoCECAR2 |
| network_name_str |
Repositorio Digital CECAR |
| repository_id_str |
|
| dc.title.eng.fl_str_mv |
A Note On Preservation Of Spectra For Two Given Operators |
| title |
A Note On Preservation Of Spectra For Two Given Operators |
| spellingShingle |
A Note On Preservation Of Spectra For Two Given Operators Restriction of an operator Spectral property Semi-Fredholm spectra Multiplication operator |
| title_short |
A Note On Preservation Of Spectra For Two Given Operators |
| title_full |
A Note On Preservation Of Spectra For Two Given Operators |
| title_fullStr |
A Note On Preservation Of Spectra For Two Given Operators |
| title_full_unstemmed |
A Note On Preservation Of Spectra For Two Given Operators |
| title_sort |
A Note On Preservation Of Spectra For Two Given Operators |
| dc.creator.fl_str_mv |
Carpintero, Carlos Gutiérrez, Alexander Rosas, Ennis Sanabria, José |
| dc.contributor.author.none.fl_str_mv |
Carpintero, Carlos Gutiérrez, Alexander Rosas, Ennis Sanabria, José |
| dc.contributor.researchgroup.none.fl_str_mv |
Ciencias, Entorno y optimización (CEO) |
| dc.subject.proposal.eng.fl_str_mv |
Restriction of an operator Spectral property Semi-Fredholm spectra Multiplication operator |
| topic |
Restriction of an operator Spectral property Semi-Fredholm spectra Multiplication operator |
| description |
We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra corresponding to two given operators are preserved. As an application of our results, we give conditions for which the above mentioned spectra corresponding to two multiplication operators acting on the space of functions of bounded p-variation in Wiener’s sense coincide. Additional illustrative results are given too. |
| publishDate |
2020 |
| dc.date.issued.none.fl_str_mv |
2020 |
| dc.date.accessioned.none.fl_str_mv |
2025-09-08T19:42:29Z |
| dc.type.none.fl_str_mv |
Artículo de revista |
| dc.type.coar.none.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.type.content.none.fl_str_mv |
Text |
| dc.type.driver.none.fl_str_mv |
info:eu-repo/semantics/article |
| dc.type.redcol.none.fl_str_mv |
http://purl.org/redcol/resource_type/ART |
| dc.type.version.none.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
| dc.type.coarversion.none.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
| format |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| status_str |
publishedVersion |
| dc.identifier.citation.none.fl_str_mv |
The author(s) 2019. This is an open access article under the CC BY-NC-ND licence |
| dc.identifier.uri.none.fl_str_mv |
https://repositorio.cecar.edu.co/handle/cecar/10907 |
| dc.identifier.eissn.none.fl_str_mv |
0862-7959 |
| identifier_str_mv |
The author(s) 2019. This is an open access article under the CC BY-NC-ND licence 0862-7959 |
| url |
https://repositorio.cecar.edu.co/handle/cecar/10907 |
| dc.language.iso.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.citationendpage.none.fl_str_mv |
126 |
| dc.relation.citationissue.none.fl_str_mv |
2 |
| dc.relation.citationstartpage.none.fl_str_mv |
113 |
| dc.relation.citationvolume.none.fl_str_mv |
145 |
| dc.relation.ispartofjournal.none.fl_str_mv |
Mathematica Bohemica |
| dc.relation.references.none.fl_str_mv |
P. Aiena: Fredholm and Local Spectral Theory, with Applications to Multipliers. Kluwer Academic Publishers, Dordrecht, 2004. P. Aiena: Quasi-Fredholm operators and localized SVEP. Acta Sci. Mat. 73 (2007), 251–263. P. Aiena, M. T. Biondi, C. Carpintero: On Drazin invertibility. Proc. Am. Math. Soc. 136 (2008), 2839-2848. F. R. Astudillo-Villaba, R. E. Castillo, J. C. Ramos-Fernández: Multiplication operators on the spaces of functions of bounded p-variation in Wiener’s sense. Real Anal. Exch. 42 (2017), 329–344 . B. A. Barnes: The spectral and Fredholm theory of extensions of bounded linear operators. Proc. Am. Math. Soc. 105 (1989), 941–949 B. A. Barnes: Restrictions of bounded linear operators: Closed range. Proc. Am. Math. Soc. 135 (2007), 1735–1740. M. Berkani: On a class of quasi-Fredholm operators. Integral Equations Oper. Theory 34 (1999), 244–249. M. Berkani, M. Sarih: On semi B-Fredholm operators. Glasg. Math. J. 43 (2001), 457–465. C. Carpintero, D. Mu˜noz, E. Rosas, J. Sanabria, O. García: Weyl type theorems and restrictions. Mediterr. J. Math. 11 (2014), 1215–1228. J. K. Finch: The single valued extension property on a Banach space. Pac. J. Math. 58 (1975), 61–69. H. G. Heuser: Functional Analysis. A Wiley-Interscience Publication. John Wiley & Sons, Chichester, 1982. |
| dc.rights.spa.fl_str_mv |
Derechos Reservados. Corporación Universitaria del Caribe – CECAR |
| dc.rights.uri.none.fl_str_mv |
https://creativecommons.org/licenses/by-nc/4.0/ |
| dc.rights.license.none.fl_str_mv |
Atribución-NoComercial 4.0 Internacional (CC BY-NC 4.0) |
| dc.rights.accessrights.none.fl_str_mv |
info:eu-repo/semantics/openAccess |
| dc.rights.coar.none.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
| rights_invalid_str_mv |
Derechos Reservados. Corporación Universitaria del Caribe – CECAR https://creativecommons.org/licenses/by-nc/4.0/ Atribución-NoComercial 4.0 Internacional (CC BY-NC 4.0) http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.extent.none.fl_str_mv |
14 paginas |
| dc.format.mimetype.none.fl_str_mv |
application/pdf |
| dc.publisher.place.none.fl_str_mv |
Colombia |
| dc.source.none.fl_str_mv |
DOI:10.21136/MB.2019.0038-18 |
| institution |
Corporación Universitaria del Caribe - CECAR |
| bitstream.url.fl_str_mv |
https://repositorio.cecar.edu.co/bitstreams/51b5aa6c-66f1-4b8f-835e-8635e429ff81/download https://repositorio.cecar.edu.co/bitstreams/604b8881-73fa-4421-90d5-44303ecaf109/download https://repositorio.cecar.edu.co/bitstreams/518b5eaa-7b19-44c8-86b6-2333d0a23c08/download https://repositorio.cecar.edu.co/bitstreams/b0f62a16-7445-4f73-a500-d294dab68d80/download |
| bitstream.checksum.fl_str_mv |
b76e7a76e24cf2f94b3ce0ae5ed275d0 58700accc25b1a785f0bc90a8800aef9 a872fb646f73b56ef59bcc8c7009d30d f19a1fd5560c2b3ab26b4a1a42e8f27c |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 |
| repository.name.fl_str_mv |
Repositorio Digital de la Corporación Universitaria Del Caribe (Cecar) |
| repository.mail.fl_str_mv |
biblioteca@cecar.edu.co |
| _version_ |
1851054151094501376 |
| spelling |
Carpintero, CarlosGutiérrez, AlexanderRosas, EnnisSanabria, JoséCiencias, Entorno y optimización (CEO)2025-09-08T19:42:29Z2020The author(s) 2019. This is an open access article under the CC BY-NC-ND licencehttps://repositorio.cecar.edu.co/handle/cecar/109070862-7959We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra corresponding to two given operators are preserved. As an application of our results, we give conditions for which the above mentioned spectra corresponding to two multiplication operators acting on the space of functions of bounded p-variation in Wiener’s sense coincide. Additional illustrative results are given too.Estadística Aplicada y OptimizaciónMatemáticas aplicadasMateriales y Entorno.Química y Física teórica14 paginasapplication/pdfengDerechos Reservados. Corporación Universitaria del Caribe – CECARhttps://creativecommons.org/licenses/by-nc/4.0/Atribución-NoComercial 4.0 Internacional (CC BY-NC 4.0)info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2DOI:10.21136/MB.2019.0038-18A Note On Preservation Of Spectra For Two Given OperatorsArtículo de revistahttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Colombia1262113145Mathematica BohemicaP. Aiena: Fredholm and Local Spectral Theory, with Applications to Multipliers. Kluwer Academic Publishers, Dordrecht, 2004.P. Aiena: Quasi-Fredholm operators and localized SVEP. Acta Sci. Mat. 73 (2007), 251–263.P. Aiena, M. T. Biondi, C. Carpintero: On Drazin invertibility. Proc. Am. Math. Soc. 136 (2008), 2839-2848.F. R. Astudillo-Villaba, R. E. Castillo, J. C. Ramos-Fernández: Multiplication operators on the spaces of functions of bounded p-variation in Wiener’s sense. Real Anal. Exch. 42 (2017), 329–344 .B. A. Barnes: The spectral and Fredholm theory of extensions of bounded linear operators. Proc. Am. Math. Soc. 105 (1989), 941–949B. A. Barnes: Restrictions of bounded linear operators: Closed range. Proc. Am. Math. Soc. 135 (2007), 1735–1740.M. Berkani: On a class of quasi-Fredholm operators. Integral Equations Oper. Theory 34 (1999), 244–249.M. Berkani, M. Sarih: On semi B-Fredholm operators. Glasg. Math. J. 43 (2001), 457–465.C. Carpintero, D. Mu˜noz, E. Rosas, J. Sanabria, O. García: Weyl type theorems and restrictions. Mediterr. J. Math. 11 (2014), 1215–1228.J. K. Finch: The single valued extension property on a Banach space. Pac. J. Math. 58 (1975), 61–69.H. G. Heuser: Functional Analysis. A Wiley-Interscience Publication. John Wiley & Sons, Chichester, 1982.Restriction of an operatorSpectral propertySemi-Fredholm spectraMultiplication operatorPublicationLICENSElicense.txtlicense.txttext/plain; charset=utf-814837https://repositorio.cecar.edu.co/bitstreams/51b5aa6c-66f1-4b8f-835e-8635e429ff81/downloadb76e7a76e24cf2f94b3ce0ae5ed275d0MD51falseAnonymousREADORIGINALmb145_2_1.pdfmb145_2_1.pdfapplication/pdf170680https://repositorio.cecar.edu.co/bitstreams/604b8881-73fa-4421-90d5-44303ecaf109/download58700accc25b1a785f0bc90a8800aef9MD52trueAnonymousREADTEXTmb145_2_1.pdf.txtmb145_2_1.pdf.txtExtracted texttext/plain32689https://repositorio.cecar.edu.co/bitstreams/518b5eaa-7b19-44c8-86b6-2333d0a23c08/downloada872fb646f73b56ef59bcc8c7009d30dMD53falseAnonymousREADTHUMBNAILmb145_2_1.pdf.jpgmb145_2_1.pdf.jpgGenerated Thumbnailimage/jpeg10438https://repositorio.cecar.edu.co/bitstreams/b0f62a16-7445-4f73-a500-d294dab68d80/downloadf19a1fd5560c2b3ab26b4a1a42e8f27cMD54falseAnonymousREADcecar/10907oai:repositorio.cecar.edu.co:cecar/109072025-09-09 03:00:23.436https://creativecommons.org/licenses/by-nc/4.0/Derechos Reservados. Corporación Universitaria del Caribe – CECARopen.accesshttps://repositorio.cecar.edu.coRepositorio Digital de la Corporación Universitaria Del Caribe (Cecar)biblioteca@cecar.edu.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 |