On a problem of Lions concerning real interpolation spaces. The quasi-Banach case

We prove that, under a mild condition on a couple (A0;A1) of quasi-Banach spaces, all real interpolation spaces (A0;A1)θ,p with 0 < θ < 1 and 0 < p ≤ ∞ are different from each other. In the Banach case and for 1 ≤ p ≤ ∞ this was shown by Janson, Nilsson, Peetre and Zafran, thus solving an o...

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Detalhes bibliográficos
Autores: Cobos Díaz, Fernando, Cwikel, M., Kühn, Thomas
Formato: artículo
Fecha de publicación:2022
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/71924
Acesso em linha:https://hdl.handle.net/20.500.14352/71924
Access Level:acceso abierto
Palavra-chave:517.98
Real interpolation
K-functional
Dependence on the parameters
Spaces of operators defined by approximation numbers.
Análisis funcional y teoría de operadores
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spelling On a problem of Lions concerning real interpolation spaces. The quasi-Banach caseCobos Díaz, FernandoCwikel, M.Kühn, Thomas517.98Real interpolationK-functionalDependence on the parametersSpaces of operators defined by approximation numbers.Análisis funcional y teoría de operadoresWe prove that, under a mild condition on a couple (A0;A1) of quasi-Banach spaces, all real interpolation spaces (A0;A1)θ,p with 0 < θ < 1 and 0 < p ≤ ∞ are different from each other. In the Banach case and for 1 ≤ p ≤ ∞ this was shown by Janson, Nilsson, Peetre and Zafran, thus solving an old problem posed by J.-L. Lions. Moreover, we give an application to certain spaces which are important objects in Operator Theory and which consist of bounded linear operators whose approximation numbers belong to Lorentz sequence spaces.ElsevierUniversidad Complutense de Madrid20222022-08-2820222022-08-28journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/71924reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Atribución-NoComercial-SinDerivadas 3.0 Españahttps://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/719242026-06-02T12:44:21Z
dc.title.none.fl_str_mv On a problem of Lions concerning real interpolation spaces. The quasi-Banach case
title On a problem of Lions concerning real interpolation spaces. The quasi-Banach case
spellingShingle On a problem of Lions concerning real interpolation spaces. The quasi-Banach case
Cobos Díaz, Fernando
517.98
Real interpolation
K-functional
Dependence on the parameters
Spaces of operators defined by approximation numbers.
Análisis funcional y teoría de operadores
title_short On a problem of Lions concerning real interpolation spaces. The quasi-Banach case
title_full On a problem of Lions concerning real interpolation spaces. The quasi-Banach case
title_fullStr On a problem of Lions concerning real interpolation spaces. The quasi-Banach case
title_full_unstemmed On a problem of Lions concerning real interpolation spaces. The quasi-Banach case
title_sort On a problem of Lions concerning real interpolation spaces. The quasi-Banach case
dc.creator.none.fl_str_mv Cobos Díaz, Fernando
Cwikel, M.
Kühn, Thomas
author Cobos Díaz, Fernando
author_facet Cobos Díaz, Fernando
Cwikel, M.
Kühn, Thomas
author_role author
author2 Cwikel, M.
Kühn, Thomas
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517.98
Real interpolation
K-functional
Dependence on the parameters
Spaces of operators defined by approximation numbers.
Análisis funcional y teoría de operadores
topic 517.98
Real interpolation
K-functional
Dependence on the parameters
Spaces of operators defined by approximation numbers.
Análisis funcional y teoría de operadores
description We prove that, under a mild condition on a couple (A0;A1) of quasi-Banach spaces, all real interpolation spaces (A0;A1)θ,p with 0 < θ < 1 and 0 < p ≤ ∞ are different from each other. In the Banach case and for 1 ≤ p ≤ ∞ this was shown by Janson, Nilsson, Peetre and Zafran, thus solving an old problem posed by J.-L. Lions. Moreover, we give an application to certain spaces which are important objects in Operator Theory and which consist of bounded linear operators whose approximation numbers belong to Lorentz sequence spaces.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-08-28
2022
2022-08-28
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/20.500.14352/71924
url https://hdl.handle.net/20.500.14352/71924
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
Atribución-NoComercial-SinDerivadas 3.0 España
https://creativecommons.org/licenses/by-nc-nd/3.0/es/
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
Atribución-NoComercial-SinDerivadas 3.0 España
https://creativecommons.org/licenses/by-nc-nd/3.0/es/
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 15.300719

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