On the hereditary character of certain spectral properties and some applications

Abstract 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 Tn(X) ⊆ W, for some n ≥ 1, where T ∈ L(X) and X is an infinite-dimensional complex Banach space. We prove t...

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Autores principales:	Carpintero,Carlos Rafael, Rosas Rodriguez,Ennis Rafael, García Mojica,Orlando J., Sanabria,José Eduardo, Malaver,Andrés
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2021
Materias:	Weyl type theorems Restrictions of operators Integral operators Spectral properties Semi-Fredholm theory
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000501053
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spelling	oai:scielo:S0716-091720210005010532021-10-05On the hereditary character of certain spectral properties and some applicationsCarpintero,Carlos RafaelRosas Rodriguez,Ennis RafaelGarcía Mojica,Orlando J.Sanabria,José EduardoMalaver,Andrés Weyl type theorems Restrictions of operators Integral operators Spectral properties Semi-Fredholm theory Abstract 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 Tn(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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.40 n.5 20212021-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000501053en10.22199/issn.0717-6279-3678
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Weyl type theorems Restrictions of operators Integral operators Spectral properties Semi-Fredholm theory
spellingShingle	Weyl type theorems Restrictions of operators Integral operators Spectral properties Semi-Fredholm theory Carpintero,Carlos Rafael Rosas Rodriguez,Ennis Rafael García Mojica,Orlando J. Sanabria,José Eduardo Malaver,Andrés On the hereditary character of certain spectral properties and some applications
description	Abstract 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 Tn(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.
author	Carpintero,Carlos Rafael Rosas Rodriguez,Ennis Rafael García Mojica,Orlando J. Sanabria,José Eduardo Malaver,Andrés
author_facet	Carpintero,Carlos Rafael Rosas Rodriguez,Ennis Rafael García Mojica,Orlando J. Sanabria,José Eduardo Malaver,Andrés
author_sort	Carpintero,Carlos Rafael
title	On the hereditary character of certain spectral properties and some applications
title_short	On the hereditary character of certain spectral properties and some applications
title_full	On the hereditary character of certain spectral properties and some applications
title_fullStr	On the hereditary character of certain spectral properties and some applications
title_full_unstemmed	On the hereditary character of certain spectral properties and some applications
title_sort	on the hereditary character of certain spectral properties and some applications
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2021
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000501053
work_keys_str_mv	AT carpinterocarlosrafael onthehereditarycharacterofcertainspectralpropertiesandsomeapplications AT rosasrodriguezennisrafael onthehereditarycharacterofcertainspectralpropertiesandsomeapplications AT garciamojicaorlandoj onthehereditarycharacterofcertainspectralpropertiesandsomeapplications AT sanabriajoseeduardo onthehereditarycharacterofcertainspectralpropertiesandsomeapplications AT malaverandres onthehereditarycharacterofcertainspectralpropertiesandsomeapplications
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On the hereditary character of certain spectral properties and some applications

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