Some properties and applications of equicompact sets of operators

Let X and Y be Banach spaces. A subset M of K(X,Y ) (the vector space of all compact operators from X into Y endowed with the operator norm) is said to be equicompact if every bounded sequence (xn) in X has a subsequence (xk(n))n such that (Txk(n))n is uniformly convergent for T ∈ M. We study the re...

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Detalhes bibliográficos
Autores: Serrano Aguilar, Enrique, Piñeiro Gómez, Cándido, Delgado Sánchez, Juan Manuel
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2007
País:España
Recursos:Universidad de Sevilla (US)
Repositório:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/96304
Acesso em linha:https://hdl.handle.net/11441/96304
https://doi.org/10.4064/sm181-2-4
Access Level:Acceso aberto
Palavra-chave:Compact operators
Equicompact sets of operators
Collectively compact set
Vector measures
Ascoli’s theorem
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spelling Some properties and applications of equicompact sets of operatorsSerrano Aguilar, EnriquePiñeiro Gómez, CándidoDelgado Sánchez, Juan ManuelCompact operatorsEquicompact sets of operatorsCollectively compact setVector measuresAscoli’s theoremLet X and Y be Banach spaces. A subset M of K(X,Y ) (the vector space of all compact operators from X into Y endowed with the operator norm) is said to be equicompact if every bounded sequence (xn) in X has a subsequence (xk(n))n such that (Txk(n))n is uniformly convergent for T ∈ M. We study the relationship between this concept and the notion of uniformly completely continuous set and give some applications. Among other results, we obtain a generalization of the classical Ascoli theorem and a compactness criterion in Mc(F,X), the Banach space of all (finitely additive) vector measures (with compact range) from a field F of sets into X endowed with the semivariation norm.Polskiej Akademii Nauk, Instytut MatematycznyMatemática Aplicada I2007info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/96304https://doi.org/10.4064/sm181-2-4reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)Inglésinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/963042026-06-17T12:51:07Z
dc.title.none.fl_str_mv Some properties and applications of equicompact sets of operators
title Some properties and applications of equicompact sets of operators
spellingShingle Some properties and applications of equicompact sets of operators
Serrano Aguilar, Enrique
Compact operators
Equicompact sets of operators
Collectively compact set
Vector measures
Ascoli’s theorem
title_short Some properties and applications of equicompact sets of operators
title_full Some properties and applications of equicompact sets of operators
title_fullStr Some properties and applications of equicompact sets of operators
title_full_unstemmed Some properties and applications of equicompact sets of operators
title_sort Some properties and applications of equicompact sets of operators
dc.creator.none.fl_str_mv Serrano Aguilar, Enrique
Piñeiro Gómez, Cándido
Delgado Sánchez, Juan Manuel
author Serrano Aguilar, Enrique
author_facet Serrano Aguilar, Enrique
Piñeiro Gómez, Cándido
Delgado Sánchez, Juan Manuel
author_role author
author2 Piñeiro Gómez, Cándido
Delgado Sánchez, Juan Manuel
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
dc.subject.none.fl_str_mv Compact operators
Equicompact sets of operators
Collectively compact set
Vector measures
Ascoli’s theorem
topic Compact operators
Equicompact sets of operators
Collectively compact set
Vector measures
Ascoli’s theorem
description Let X and Y be Banach spaces. A subset M of K(X,Y ) (the vector space of all compact operators from X into Y endowed with the operator norm) is said to be equicompact if every bounded sequence (xn) in X has a subsequence (xk(n))n such that (Txk(n))n is uniformly convergent for T ∈ M. We study the relationship between this concept and the notion of uniformly completely continuous set and give some applications. Among other results, we obtain a generalization of the classical Ascoli theorem and a compactness criterion in Mc(F,X), the Banach space of all (finitely additive) vector measures (with compact range) from a field F of sets into X endowed with the semivariation norm.
publishDate 2007
dc.date.none.fl_str_mv 2007
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/96304
https://doi.org/10.4064/sm181-2-4
url https://hdl.handle.net/11441/96304
https://doi.org/10.4064/sm181-2-4
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Polskiej Akademii Nauk, Instytut Matematyczny
publisher.none.fl_str_mv Polskiej Akademii Nauk, Instytut Matematyczny
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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