Power-regular Bishop operators and spectral decompositions

It is proved that a wide class of Bishop-type operators $T_{\phi,\tau}$ are power-regular operators in $L^p(\Omega, \mu)$, $1 \leq p < \infty$, computing the exact value of the local spectral radius at any function $u \in L^p(\Omega, \mu)$. Moreover, it is shown that the local spectral radius at...

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Detalles Bibliográficos
Autores: Gallardo Gutiérrez, Eva Antonia, Monsalve López, Miguel
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/129352
Acceso en línea:https://hdl.handle.net/20.500.14352/129352
Access Level:acceso abierto
Palabra clave:Bishop operators
Decomposable operators
Power-regular operators
Análisis funcional y teoría de operadores
1202.03 Álgebra y Espacios de Banach
1202.14 Espacio de Hilbert
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spelling Power-regular Bishop operators and spectral decompositionsGallardo Gutiérrez, Eva AntoniaMonsalve López, MiguelBishop operatorsDecomposable operatorsPower-regular operatorsAnálisis funcional y teoría de operadores1202.03 Álgebra y Espacios de Banach1202.14 Espacio de HilbertIt is proved that a wide class of Bishop-type operators $T_{\phi,\tau}$ are power-regular operators in $L^p(\Omega, \mu)$, $1 \leq p < \infty$, computing the exact value of the local spectral radius at any function $u \in L^p(\Omega, \mu)$. Moreover, it is shown that the local spectral radius at any $u$ coincides with the spectral radius of $T_{\phi,\tau}$ as far as u is non-zero. As a consequence, it is proved that non-invertible Bishop-type operators are non-decomposable whenever $\log|\phi| \in L^1(\Omega, \mu)$ (in particular, not quasinilpotent); not enjoying even the weaker spectral decompositions Bishop property $(\beta)$ and property $(\delta)$.Theta FoundationUniversidad Complutense de Madrid20212021-01-0120212021-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/129352reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/1293522026-06-02T12:44:21Z
dc.title.none.fl_str_mv Power-regular Bishop operators and spectral decompositions
title Power-regular Bishop operators and spectral decompositions
spellingShingle Power-regular Bishop operators and spectral decompositions
Gallardo Gutiérrez, Eva Antonia
Bishop operators
Decomposable operators
Power-regular operators
Análisis funcional y teoría de operadores
1202.03 Álgebra y Espacios de Banach
1202.14 Espacio de Hilbert
title_short Power-regular Bishop operators and spectral decompositions
title_full Power-regular Bishop operators and spectral decompositions
title_fullStr Power-regular Bishop operators and spectral decompositions
title_full_unstemmed Power-regular Bishop operators and spectral decompositions
title_sort Power-regular Bishop operators and spectral decompositions
dc.creator.none.fl_str_mv Gallardo Gutiérrez, Eva Antonia
Monsalve López, Miguel
author Gallardo Gutiérrez, Eva Antonia
author_facet Gallardo Gutiérrez, Eva Antonia
Monsalve López, Miguel
author_role author
author2 Monsalve López, Miguel
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv Bishop operators
Decomposable operators
Power-regular operators
Análisis funcional y teoría de operadores
1202.03 Álgebra y Espacios de Banach
1202.14 Espacio de Hilbert
topic Bishop operators
Decomposable operators
Power-regular operators
Análisis funcional y teoría de operadores
1202.03 Álgebra y Espacios de Banach
1202.14 Espacio de Hilbert
description It is proved that a wide class of Bishop-type operators $T_{\phi,\tau}$ are power-regular operators in $L^p(\Omega, \mu)$, $1 \leq p < \infty$, computing the exact value of the local spectral radius at any function $u \in L^p(\Omega, \mu)$. Moreover, it is shown that the local spectral radius at any $u$ coincides with the spectral radius of $T_{\phi,\tau}$ as far as u is non-zero. As a consequence, it is proved that non-invertible Bishop-type operators are non-decomposable whenever $\log|\phi| \in L^1(\Omega, \mu)$ (in particular, not quasinilpotent); not enjoying even the weaker spectral decompositions Bishop property $(\beta)$ and property $(\delta)$.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-01-01
2021
2021-01-01
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/20.500.14352/129352
url https://hdl.handle.net/20.500.14352/129352
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
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
eu_rights_str_mv openAccess
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: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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score 15,812455

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