Finite rank perturbations of normal operators: spectral idempotents and decomposability

We prove that a large class of finite rank perturbations of diagonal operators and, in general, of diagonalizable normal operators of multiplicity one acting boundedly on a separable, infinite dimensional complex Hilbert space are decomposable operators in the sense of Colojoară and Foiaş [1]. Conse...

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Detalles Bibliográficos
Autores: Gallardo Gutiérrez, Eva Antonia, González Doña, F. Javier
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/87560
Acceso en línea:https://hdl.handle.net/20.500.14352/87560
Access Level:acceso abierto
Palabra clave:51
Finite rank perturbations of normal operators
Invariant subspaces
Spectral subspaces
Decomposable operators
Matemáticas (Matemáticas)
12 Matemáticas
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spelling Finite rank perturbations of normal operators: spectral idempotents and decomposabilityGallardo Gutiérrez, Eva AntoniaGonzález Doña, F. Javier51Finite rank perturbations of normal operatorsInvariant subspacesSpectral subspacesDecomposable operatorsMatemáticas (Matemáticas)12 MatemáticasWe prove that a large class of finite rank perturbations of diagonal operators and, in general, of diagonalizable normal operators of multiplicity one acting boundedly on a separable, infinite dimensional complex Hilbert space are decomposable operators in the sense of Colojoară and Foiaş [1]. Consequently, every operator T in such a class has a rich spectral structure and plenty of non-trivial closed hyperinvariant subspaces which extends, in particular, previous theorems of Foiaş, Jung, Ko and Pearcy [5], [6], [7], Fang and J. Xia [3] and the authors [8], [9] on an open question posed by Pearcy in the seventies.ELSEVIERUniversidad Complutense de Madrid20232023-08-3020232023-08-30journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/87560reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/875602026-06-02T12:44:21Z
dc.title.none.fl_str_mv Finite rank perturbations of normal operators: spectral idempotents and decomposability
title Finite rank perturbations of normal operators: spectral idempotents and decomposability
spellingShingle Finite rank perturbations of normal operators: spectral idempotents and decomposability
Gallardo Gutiérrez, Eva Antonia
51
Finite rank perturbations of normal operators
Invariant subspaces
Spectral subspaces
Decomposable operators
Matemáticas (Matemáticas)
12 Matemáticas
title_short Finite rank perturbations of normal operators: spectral idempotents and decomposability
title_full Finite rank perturbations of normal operators: spectral idempotents and decomposability
title_fullStr Finite rank perturbations of normal operators: spectral idempotents and decomposability
title_full_unstemmed Finite rank perturbations of normal operators: spectral idempotents and decomposability
title_sort Finite rank perturbations of normal operators: spectral idempotents and decomposability
dc.creator.none.fl_str_mv Gallardo Gutiérrez, Eva Antonia
González Doña, F. Javier
author Gallardo Gutiérrez, Eva Antonia
author_facet Gallardo Gutiérrez, Eva Antonia
González Doña, F. Javier
author_role author
author2 González Doña, F. Javier
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 51
Finite rank perturbations of normal operators
Invariant subspaces
Spectral subspaces
Decomposable operators
Matemáticas (Matemáticas)
12 Matemáticas
topic 51
Finite rank perturbations of normal operators
Invariant subspaces
Spectral subspaces
Decomposable operators
Matemáticas (Matemáticas)
12 Matemáticas
description We prove that a large class of finite rank perturbations of diagonal operators and, in general, of diagonalizable normal operators of multiplicity one acting boundedly on a separable, infinite dimensional complex Hilbert space are decomposable operators in the sense of Colojoară and Foiaş [1]. Consequently, every operator T in such a class has a rich spectral structure and plenty of non-trivial closed hyperinvariant subspaces which extends, in particular, previous theorems of Foiaş, Jung, Ko and Pearcy [5], [6], [7], Fang and J. Xia [3] and the authors [8], [9] on an open question posed by Pearcy in the seventies.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-08-30
2023
2023-08-30
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/87560
url https://hdl.handle.net/20.500.14352/87560
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv ELSEVIER
publisher.none.fl_str_mv ELSEVIER
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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