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 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.

• Autores: Carpintero, Rafael; ROSAS, ENNIS; García, Orlando; Sanabria, José; Malaver, Andrés
• Tipo de recurso: Article of journal
• Fecha de publicación: 2021
• Institución: Corporación Universidad de la Costa
• Repositorio: REDICUC - Repositorio CUC
• Idioma: eng
• OAI Identifier: oai:repositorio.cuc.edu.co:11323/8836
• Acceso en línea: https://hdl.handle.net/11323/8836; https://doi.org/10.22199/issn.0717-6279-3678; https://repositorio.cuc.edu.co/
• Palabra clave: Weyl type theorems; Restrictions of operators; Integral operators; Spectral properties; Semi-Fredholm theory
• Rights: openAccess
• License: CC0 1.0 Universal