On the hereditary character of certain spectral properties and some applications
In this paper we study the behavior of certain spectral properties of an operator T on a proper closed and T-invariant subspace W ⊆ X such that T n(X) ⊆ W, for some n ≥ 1, where T ∈ L(X) and X is an infinite-dimensional complex Banach space. We prove that for these subspaces a large number of spectr...
- Autores:
-
Carpintero, Carlos
Garcia, Orlando
Rosas, Ennis
Sanabria, J
Malaver, A
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2021
- Institución:
- Corporación Universitaria del Caribe - CECAR
- Repositorio:
- Repositorio Digital CECAR
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.cecar.edu.co:cecar/10895
- Acceso en línea:
- https://repositorio.cecar.edu.co/handle/cecar/10895
- Palabra clave:
- Weyl type theorems
Restrictions of operators
Integral operators
Spectral properties
Semi-Fredholm theory
- Rights
- openAccess
- License
- Derechos Reservados. Corporación Universitaria del Caribe – CECAR
| Summary: | In this paper we study the behavior of certain spectral properties of an operator T on a proper closed and T-invariant subspace W ⊆ X such that T n(X) ⊆ W, for some n ≥ 1, where T ∈ L(X) and X is an infinite-dimensional complex Banach space. We prove that for these subspaces a large number of spectral properties are transmitted from T to its restriction on W and vice-versa. As consequence of our results, we give conditions for which semi-Fredholm spectral properties, as well as Weyl type theorems, are equivalent for two given operators. Additionally, we give conditions under which an operator acting on a subspace can be extended on the entire space preserving the Weyl type theorems. In particular, we give some applications of these results for integral operators acting on certain functions spaces. |
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