Spectral dissection of finite rank perturbations of normal operators

Finite rank perturbations T = N + K of a bounded normal operator N on a separable Hilbert space are studied thanks to a natural functional model of T ; in its turn the functional model solely relies on a perturbation matrix/ characteristic function previously defined by the second author. Function t...

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Detalhes bibliográficos
Autores: Putinar, Mihai, Yakubóvich Lazarev, Dmitry
Formato: artículo
Fecha de publicación:2021
País:España
Recursos:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/731780
Acesso em linha:https://hdl.handle.net/10486/731780
https://dx.doi.org/10.7900/jot.2019jul21.2266
Access Level:acceso embargado
Palavra-chave:Bishop’s property (β)
decomposable operator
functional model
perturbation determinant
normal operator
Matemáticas
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spelling Spectral dissection of finite rank perturbations of normal operatorsPutinar, MihaiYakubóvich Lazarev, DmitryBishop’s property (β)decomposable operatorfunctional modelperturbation determinantnormal operatorMatemáticasFinite rank perturbations T = N + K of a bounded normal operator N on a separable Hilbert space are studied thanks to a natural functional model of T ; in its turn the functional model solely relies on a perturbation matrix/ characteristic function previously defined by the second author. Function theoretic features of this perturbation matrix encode in a closed-form the spectral behavior of T . Under mild geometric conditions on the spectral measure of N and some smoothness constraints on K we show that the operator T admits invariant subspaces, or even it is decomposableThe authors acknowledge partial support by Spanish Ministry of Science, Innovation and Universities (grant no. PGC2018-099124-B-I00), the ICMAT Severo Ochoa project SEV-2015-0554 of the Spanish Ministry of Economy and Competitiveness of Spain and the European Regional Development Fund. The first author expresses his gratitude to the Universidad Autonoma de Madrid for hospitality. We are both grateful to the Mittag-Leffler Institute for offering the opportunity to progress on this projectTheta FoundationFacultad de CienciasDepartamento de MatemáticasTeoría Espectral de Operadores. Aplicaciones a Ecuaciones en derivadas Parciales y a Sistemas DinámicosAgencia Estatal de Investigación20212021-12-31research articlehttp://purl.org/coar/resource_type/c_2df8fbb1AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10486/731780https://dx.doi.org/10.7900/jot.2019jul21.2266reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengembargoed accesshttp://purl.org/coar/access_right/c_f1cfinfo:eu-repo/semantics/embargoedAccessoai:repositorio.uam.es:10486/7317802026-06-23T12:46:27Z
dc.title.none.fl_str_mv Spectral dissection of finite rank perturbations of normal operators
title Spectral dissection of finite rank perturbations of normal operators
spellingShingle Spectral dissection of finite rank perturbations of normal operators
Putinar, Mihai
Bishop’s property (β)
decomposable operator
functional model
perturbation determinant
normal operator
Matemáticas
title_short Spectral dissection of finite rank perturbations of normal operators
title_full Spectral dissection of finite rank perturbations of normal operators
title_fullStr Spectral dissection of finite rank perturbations of normal operators
title_full_unstemmed Spectral dissection of finite rank perturbations of normal operators
title_sort Spectral dissection of finite rank perturbations of normal operators
dc.creator.none.fl_str_mv Putinar, Mihai
Yakubóvich Lazarev, Dmitry
author Putinar, Mihai
author_facet Putinar, Mihai
Yakubóvich Lazarev, Dmitry
author_role author
author2 Yakubóvich Lazarev, Dmitry
author2_role author
dc.contributor.none.fl_str_mv Facultad de Ciencias
Departamento de Matemáticas
Teoría Espectral de Operadores. Aplicaciones a Ecuaciones en derivadas Parciales y a Sistemas Dinámicos
Agencia Estatal de Investigación
dc.subject.none.fl_str_mv Bishop’s property (β)
decomposable operator
functional model
perturbation determinant
normal operator
Matemáticas
topic Bishop’s property (β)
decomposable operator
functional model
perturbation determinant
normal operator
Matemáticas
description Finite rank perturbations T = N + K of a bounded normal operator N on a separable Hilbert space are studied thanks to a natural functional model of T ; in its turn the functional model solely relies on a perturbation matrix/ characteristic function previously defined by the second author. Function theoretic features of this perturbation matrix encode in a closed-form the spectral behavior of T . Under mild geometric conditions on the spectral measure of N and some smoothness constraints on K we show that the operator T admits invariant subspaces, or even it is decomposable
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-12-31
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10486/731780
https://dx.doi.org/10.7900/jot.2019jul21.2266
url https://hdl.handle.net/10486/731780
https://dx.doi.org/10.7900/jot.2019jul21.2266
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv embargoed access
http://purl.org/coar/access_right/c_f1cf
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/embargoedAccess
rights_invalid_str_mv embargoed access
http://purl.org/coar/access_right/c_f1cf
eu_rights_str_mv embargoedAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Theta Foundation
publisher.none.fl_str_mv Theta Foundation
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
repository.name.fl_str_mv
repository.mail.fl_str_mv
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