Regular fractional weighted Wiener algebras and invariant subspaces

Since the fififties, the interplay between spectral theory, harmonic analysis and a wide variety of techniques based on the functional calculus of operators, has provided useful criteria to find non-trivial closed invariant subspaces for operators acting on complex Banach spaces. In this article, so...

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Authors: Abadias, Luciano, Monsalve López, Miguel
Format: article
Publication Date:2026
Country:España
Institution:Universidad Complutense de Madrid (UCM)
Repository:Docta Complutense
Language:English
OAI Identifier:oai:docta.ucm.es:20.500.14352/129006
Online Access:https://hdl.handle.net/20.500.14352/129006
Access Level:Open access
Keyword:Cesàro summability
Regular Wiener algebras
Functional calculus
Invariant subspaces
Análisis funcional y teoría de operadores
Análisis matemático
1202.03 Álgebra y Espacios de Banach
1202.13 Análisis Armónico
1202.14 Espacio de Hilbert
1202.01 Álgebra de Operadores
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oai_identifier_str oai:docta.ucm.es:20.500.14352/129006
network_acronym_str ES
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repository_id_str
spelling Regular fractional weighted Wiener algebras and invariant subspacesAbadias, LucianoMonsalve López, MiguelCesàro summabilityRegular Wiener algebrasFunctional calculusInvariant subspacesAnálisis funcional y teoría de operadoresAnálisis matemático1202.03 Álgebra y Espacios de Banach1202.13 Análisis Armónico1202.14 Espacio de Hilbert1202.01 Álgebra de OperadoresSince the fififties, the interplay between spectral theory, harmonic analysis and a wide variety of techniques based on the functional calculus of operators, has provided useful criteria to find non-trivial closed invariant subspaces for operators acting on complex Banach spaces. In this article, some standard summability methods (mainly the Cesàro summation) are applied to generalize classical results due to Wermer [51] and Atzmon [8] regarding the existence of invariant subspaces under growth conditions on the resolvent of an operator. To do so, an extension of Beurling’s regularity criterion [13] is proved for fractional weighted Wiener algebras $\mathcal{A}_\rho^\alpha$ related with the Cesàro summation of order $\alpha \geq 0$. At the end of the article, other summability methods are considered for the purpose of fifinding new sufficient criteria which ensure the existence of invariant subspaces, resulting in several open questions on the regularity of fractional weighted Wiener algebras $\mathcal{A}_\rho^\mu$ associated to matrix summation methods defifined from non-vanishing complex sequences.ElsevierUniversidad Complutense de Madrid20262026-01-0120262026-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/129006reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023 PID2022-137294NB-I00 METODOS ANALITICOS Y GEOMETRICOS EN TEORIA DE OPERADORESopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/1290062026-06-02T12:44:21Z
dc.title.none.fl_str_mv Regular fractional weighted Wiener algebras and invariant subspaces
title Regular fractional weighted Wiener algebras and invariant subspaces
spellingShingle Regular fractional weighted Wiener algebras and invariant subspaces
Abadias, Luciano
Cesàro summability
Regular Wiener algebras
Functional calculus
Invariant subspaces
Análisis funcional y teoría de operadores
Análisis matemático
1202.03 Álgebra y Espacios de Banach
1202.13 Análisis Armónico
1202.14 Espacio de Hilbert
1202.01 Álgebra de Operadores
title_short Regular fractional weighted Wiener algebras and invariant subspaces
title_full Regular fractional weighted Wiener algebras and invariant subspaces
title_fullStr Regular fractional weighted Wiener algebras and invariant subspaces
title_full_unstemmed Regular fractional weighted Wiener algebras and invariant subspaces
title_sort Regular fractional weighted Wiener algebras and invariant subspaces
dc.creator.none.fl_str_mv Abadias, Luciano
Monsalve López, Miguel
author Abadias, Luciano
author_facet Abadias, Luciano
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 Cesàro summability
Regular Wiener algebras
Functional calculus
Invariant subspaces
Análisis funcional y teoría de operadores
Análisis matemático
1202.03 Álgebra y Espacios de Banach
1202.13 Análisis Armónico
1202.14 Espacio de Hilbert
1202.01 Álgebra de Operadores
topic Cesàro summability
Regular Wiener algebras
Functional calculus
Invariant subspaces
Análisis funcional y teoría de operadores
Análisis matemático
1202.03 Álgebra y Espacios de Banach
1202.13 Análisis Armónico
1202.14 Espacio de Hilbert
1202.01 Álgebra de Operadores
description Since the fififties, the interplay between spectral theory, harmonic analysis and a wide variety of techniques based on the functional calculus of operators, has provided useful criteria to find non-trivial closed invariant subspaces for operators acting on complex Banach spaces. In this article, some standard summability methods (mainly the Cesàro summation) are applied to generalize classical results due to Wermer [51] and Atzmon [8] regarding the existence of invariant subspaces under growth conditions on the resolvent of an operator. To do so, an extension of Beurling’s regularity criterion [13] is proved for fractional weighted Wiener algebras $\mathcal{A}_\rho^\alpha$ related with the Cesàro summation of order $\alpha \geq 0$. At the end of the article, other summability methods are considered for the purpose of fifinding new sufficient criteria which ensure the existence of invariant subspaces, resulting in several open questions on the regularity of fractional weighted Wiener algebras $\mathcal{A}_\rho^\mu$ associated to matrix summation methods defifined from non-vanishing complex sequences.
publishDate 2026
dc.date.none.fl_str_mv 2026
2026-01-01
2026
2026-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/129006
url https://hdl.handle.net/20.500.14352/129006
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023 PID2022-137294NB-I00 METODOS ANALITICOS Y GEOMETRICOS EN TEORIA DE OPERADORES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/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 4.0 International
http://creativecommons.org/licenses/by/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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score 15,198674

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