Left and right generalized Drazin invertible operators and local spectral theory

Abstract In this paper, we give some characterizations of the left and right generalized Drazin invertible bounded operators in Banach spaces by means of the single-valued extension property (SVEP). In particular, we show that a bounded operator is left (resp. right) generalized Drazin invertible if...

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Autores principales:	Benharrat,Mohammed, Hocine,Kouider Miloud, Messirdi,Bekkai
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2019
Materias:	Left and right generalized Drazin invertible operators Generalized Drazin invertible operators SVEP Local spectral theory.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000500897
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spelling	oai:scielo:S0716-091720190005008972020-01-07Left and right generalized Drazin invertible operators and local spectral theoryBenharrat,MohammedHocine,Kouider MiloudMessirdi,Bekkai Left and right generalized Drazin invertible operators Generalized Drazin invertible operators SVEP Local spectral theory. Abstract In this paper, we give some characterizations of the left and right generalized Drazin invertible bounded operators in Banach spaces by means of the single-valued extension property (SVEP). In particular, we show that a bounded operator is left (resp. right) generalized Drazin invertible if and only if admits a generalized Kato decomposition and has the SVEP at 0 (resp. it admits a generalized Kato decomposition and its adjoint has the SVEP at 0. In addition, we prove that both of the left and the right generalized Drazin operators are invariant under additive commuting finite rank perturbations. Furthermore, we investigate the transmission of some local spectral properties from a bounded linear operator, as the SVEP, Dunford property (C), and property (β), to its generalized Drazin inverse.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.38 n.5 20192019-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000500897en10.22199/issn.0717-6279-2019-05-0058
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Left and right generalized Drazin invertible operators Generalized Drazin invertible operators SVEP Local spectral theory.
spellingShingle	Left and right generalized Drazin invertible operators Generalized Drazin invertible operators SVEP Local spectral theory. Benharrat,Mohammed Hocine,Kouider Miloud Messirdi,Bekkai Left and right generalized Drazin invertible operators and local spectral theory
description	Abstract In this paper, we give some characterizations of the left and right generalized Drazin invertible bounded operators in Banach spaces by means of the single-valued extension property (SVEP). In particular, we show that a bounded operator is left (resp. right) generalized Drazin invertible if and only if admits a generalized Kato decomposition and has the SVEP at 0 (resp. it admits a generalized Kato decomposition and its adjoint has the SVEP at 0. In addition, we prove that both of the left and the right generalized Drazin operators are invariant under additive commuting finite rank perturbations. Furthermore, we investigate the transmission of some local spectral properties from a bounded linear operator, as the SVEP, Dunford property (C), and property (β), to its generalized Drazin inverse.
author	Benharrat,Mohammed Hocine,Kouider Miloud Messirdi,Bekkai
author_facet	Benharrat,Mohammed Hocine,Kouider Miloud Messirdi,Bekkai
author_sort	Benharrat,Mohammed
title	Left and right generalized Drazin invertible operators and local spectral theory
title_short	Left and right generalized Drazin invertible operators and local spectral theory
title_full	Left and right generalized Drazin invertible operators and local spectral theory
title_fullStr	Left and right generalized Drazin invertible operators and local spectral theory
title_full_unstemmed	Left and right generalized Drazin invertible operators and local spectral theory
title_sort	left and right generalized drazin invertible operators and local spectral theory
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2019
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000500897
work_keys_str_mv	AT benharratmohammed leftandrightgeneralizeddrazininvertibleoperatorsandlocalspectraltheory AT hocinekouidermiloud leftandrightgeneralizeddrazininvertibleoperatorsandlocalspectraltheory AT messirdibekkai leftandrightgeneralizeddrazininvertibleoperatorsandlocalspectraltheory
_version_	1718439858991529984

Left and right generalized Drazin invertible operators and local spectral theory

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