On compactness theorems for logarithmic interpolation methods

Let (A0;A1) be a Banach couple, (B0;B1) a quasi-Banach couple, 0 < q <= ∞ and T a linear operator. We prove that if T : A0 -> B0 is bounded and T : A1 -> B1 is compact, then the interpolated operator by the logarithmic method T : (A0,A1)1;q;A -> (B0;B1)1;q;A is compact too. This resul...

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Detalhes bibliográficos
Autor: Besoy, Blanca F.
Tipo de documento: artigo
Data de publicação:2019
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositório:Docta Complutense
Idioma:inglês
OAI Identifier:oai:docta.ucm.es:20.500.14352/13541
Acesso em linha:https://hdl.handle.net/20.500.14352/13541
Access Level:Acceso aberto
Palavra-chave:517.98
Logarithmic interpolation methods
compact operators
Lorentz-Zygmund spaces.
Análisis funcional y teoría de operadores
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spelling On compactness theorems for logarithmic interpolation methodsBesoy, Blanca F.517.98Logarithmic interpolation methodscompact operatorsLorentz-Zygmund spaces.Análisis funcional y teoría de operadoresLet (A0;A1) be a Banach couple, (B0;B1) a quasi-Banach couple, 0 < q <= ∞ and T a linear operator. We prove that if T : A0 -> B0 is bounded and T : A1 -> B1 is compact, then the interpolated operator by the logarithmic method T : (A0,A1)1;q;A -> (B0;B1)1;q;A is compact too. This result allows the extension of some limit variants of Krasnosel'skii's compact interpolation theorem.Polskiej Akademii Nauk, Instytut Matematyczny (Polish Academy of Sciences, Institute of Mathematics)Universidad Complutense de Madrid20192019-01-0120192019-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/13541reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/135412026-06-02T12:44:21Z
dc.title.none.fl_str_mv On compactness theorems for logarithmic interpolation methods
title On compactness theorems for logarithmic interpolation methods
spellingShingle On compactness theorems for logarithmic interpolation methods
Besoy, Blanca F.
517.98
Logarithmic interpolation methods
compact operators
Lorentz-Zygmund spaces.
Análisis funcional y teoría de operadores
title_short On compactness theorems for logarithmic interpolation methods
title_full On compactness theorems for logarithmic interpolation methods
title_fullStr On compactness theorems for logarithmic interpolation methods
title_full_unstemmed On compactness theorems for logarithmic interpolation methods
title_sort On compactness theorems for logarithmic interpolation methods
dc.creator.none.fl_str_mv Besoy, Blanca F.
author Besoy, Blanca F.
author_facet Besoy, Blanca F.
author_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517.98
Logarithmic interpolation methods
compact operators
Lorentz-Zygmund spaces.
Análisis funcional y teoría de operadores
topic 517.98
Logarithmic interpolation methods
compact operators
Lorentz-Zygmund spaces.
Análisis funcional y teoría de operadores
description Let (A0;A1) be a Banach couple, (B0;B1) a quasi-Banach couple, 0 < q <= ∞ and T a linear operator. We prove that if T : A0 -> B0 is bounded and T : A1 -> B1 is compact, then the interpolated operator by the logarithmic method T : (A0,A1)1;q;A -> (B0;B1)1;q;A is compact too. This result allows the extension of some limit variants of Krasnosel'skii's compact interpolation theorem.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01
2019
2019-01-01
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/20.500.14352/13541
url https://hdl.handle.net/20.500.14352/13541
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 Polskiej Akademii Nauk, Instytut Matematyczny (Polish Academy of Sciences, Institute of Mathematics)
publisher.none.fl_str_mv Polskiej Akademii Nauk, Instytut Matematyczny (Polish Academy of Sciences, Institute of Mathematics)
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 15,300719

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