Vector measures: where are their integrals?

Let ν be a vector measure with values in a Banach space Z. The integration map Iν:L1(ν)→Z, given by f↦∫fdν for f ∈ L 1(ν), always has a formal extension to its bidual operator I∗∗ν:L1(ν)∗∗→Z∗∗. So, we may consider the “integral” of any element f ** of L 1(ν)** as I **ν(f **). Our aim is to identify...

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Detalhes bibliográficos
Autores: Curbera Costello, Guillermo, Delgado Garrido, Olvido, Ricker, Werner J.
Tipo de documento: artigo
Estado:Versión enviada para evaluación y publicación
Data de publicação:2009
País:España
Recursos:Universidad de Sevilla (US)
Repositório:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/103784
Acesso em linha:https://hdl.handle.net/11441/103784
https://doi.org/10.1007/s11117-008-2191-1
Access Level:Acceso aberto
Palavra-chave:Banach lattices and function spaces
Vector measure
Integration map
Duality
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spelling Vector measures: where are their integrals?Curbera Costello, GuillermoDelgado Garrido, OlvidoRicker, Werner J.Banach lattices and function spacesVector measureIntegration mapDualityLet ν be a vector measure with values in a Banach space Z. The integration map Iν:L1(ν)→Z, given by f↦∫fdν for f ∈ L 1(ν), always has a formal extension to its bidual operator I∗∗ν:L1(ν)∗∗→Z∗∗. So, we may consider the “integral” of any element f ** of L 1(ν)** as I **ν(f **). Our aim is to identify when these integrals lie in more tractable subspaces Y of Z **. For Z a Banach function space X, we consider this question when Y is any one of the subspaces of X ** given by the corresponding identifications of X, X′′ (the Köthe bidual of X) and X′* (the topological dual of the Köthe dual of X). Also, we consider certain kernel operators T and study the extended operator I **ν for the particular vector measure ν defined by ν(A) := T(χ A ).Ministerio de Educación y Ciencia MTM2006-13000-C03-01SpringerMatemática Aplicada IMinisterio de Educación y Ciencia (MEC). España2009info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/103784https://doi.org/10.1007/s11117-008-2191-1reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésPositivity, 13 (1), 61-87.MTM2006-13000-C03-01https://link.springer.com/article/10.1007/s11117-008-2191-1info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1037842026-06-17T12:51:07Z
dc.title.none.fl_str_mv Vector measures: where are their integrals?
title Vector measures: where are their integrals?
spellingShingle Vector measures: where are their integrals?
Curbera Costello, Guillermo
Banach lattices and function spaces
Vector measure
Integration map
Duality
title_short Vector measures: where are their integrals?
title_full Vector measures: where are their integrals?
title_fullStr Vector measures: where are their integrals?
title_full_unstemmed Vector measures: where are their integrals?
title_sort Vector measures: where are their integrals?
dc.creator.none.fl_str_mv Curbera Costello, Guillermo
Delgado Garrido, Olvido
Ricker, Werner J.
author Curbera Costello, Guillermo
author_facet Curbera Costello, Guillermo
Delgado Garrido, Olvido
Ricker, Werner J.
author_role author
author2 Delgado Garrido, Olvido
Ricker, Werner J.
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
Ministerio de Educación y Ciencia (MEC). España
dc.subject.none.fl_str_mv Banach lattices and function spaces
Vector measure
Integration map
Duality
topic Banach lattices and function spaces
Vector measure
Integration map
Duality
description Let ν be a vector measure with values in a Banach space Z. The integration map Iν:L1(ν)→Z, given by f↦∫fdν for f ∈ L 1(ν), always has a formal extension to its bidual operator I∗∗ν:L1(ν)∗∗→Z∗∗. So, we may consider the “integral” of any element f ** of L 1(ν)** as I **ν(f **). Our aim is to identify when these integrals lie in more tractable subspaces Y of Z **. For Z a Banach function space X, we consider this question when Y is any one of the subspaces of X ** given by the corresponding identifications of X, X′′ (the Köthe bidual of X) and X′* (the topological dual of the Köthe dual of X). Also, we consider certain kernel operators T and study the extended operator I **ν for the particular vector measure ν defined by ν(A) := T(χ A ).
publishDate 2009
dc.date.none.fl_str_mv 2009
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/103784
https://doi.org/10.1007/s11117-008-2191-1
url https://hdl.handle.net/11441/103784
https://doi.org/10.1007/s11117-008-2191-1
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Positivity, 13 (1), 61-87.
MTM2006-13000-C03-01
https://link.springer.com/article/10.1007/s11117-008-2191-1
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 Springer
publisher.none.fl_str_mv Springer
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 15.300724

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