Biduals of tensor products in operator spaces

Autores
Dimant, Veronica Isabel; Fernández Unzueta, Maite
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study whether the operator space V ∗∗ α ⊗ W∗∗ can be identified with a subspace of the bidual space (V α ⊗ W) ∗∗, for a given operator space tensor norm. We prove that this can be done if α is finitely generated and V and W are locally reflexive. If in addition the dual spaces are locally reflexive and the bidual spaces have the completely bounded approximation property, then the identification is through a complete isomorphism. When α is the projective, Haagerup or injective norm, the hypotheses can be weakened.
Fil: Dimant, Veronica Isabel. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Fernández Unzueta, Maite. Centro de Investigación en Matemáticas; México
Materia
Operator Spaces
Tensor Products
Bilinear Mappings
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/42352
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Biduals of tensor products in operator spacesDimant, Veronica IsabelFernández Unzueta, MaiteOperator SpacesTensor ProductsBilinear Mappingshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study whether the operator space V ∗∗ α ⊗ W∗∗ can be identified with a subspace of the bidual space (V α ⊗ W) ∗∗, for a given operator space tensor norm. We prove that this can be done if α is finitely generated and V and W are locally reflexive. If in addition the dual spaces are locally reflexive and the bidual spaces have the completely bounded approximation property, then the identification is through a complete isomorphism. When α is the projective, Haagerup or injective norm, the hypotheses can be weakened.Fil: Dimant, Veronica Isabel. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Fernández Unzueta, Maite. Centro de Investigación en Matemáticas; MéxicoPolish Academy of Sciences. Institute of Mathematics2015-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/42352Dimant, Veronica Isabel; Fernández Unzueta, Maite; Biduals of tensor products in operator spaces; Polish Academy of Sciences. Institute of Mathematics; Studia Mathematica; 230; 2; 12-2015; 165-1850039-3223CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8292-1-2016info:eu-repo/semantics/altIdentifier/doi/10.4064/sm8292-1-2016info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:47:02Zoai:ri.conicet.gov.ar:11336/42352instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:47:02.313CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Biduals of tensor products in operator spaces
title Biduals of tensor products in operator spaces
spellingShingle Biduals of tensor products in operator spaces
Dimant, Veronica Isabel
Operator Spaces
Tensor Products
Bilinear Mappings
title_short Biduals of tensor products in operator spaces
title_full Biduals of tensor products in operator spaces
title_fullStr Biduals of tensor products in operator spaces
title_full_unstemmed Biduals of tensor products in operator spaces
title_sort Biduals of tensor products in operator spaces
dc.creator.none.fl_str_mv Dimant, Veronica Isabel
Fernández Unzueta, Maite
author Dimant, Veronica Isabel
author_facet Dimant, Veronica Isabel
Fernández Unzueta, Maite
author_role author
author2 Fernández Unzueta, Maite
author2_role author
dc.subject.none.fl_str_mv Operator Spaces
Tensor Products
Bilinear Mappings
topic Operator Spaces
Tensor Products
Bilinear Mappings
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study whether the operator space V ∗∗ α ⊗ W∗∗ can be identified with a subspace of the bidual space (V α ⊗ W) ∗∗, for a given operator space tensor norm. We prove that this can be done if α is finitely generated and V and W are locally reflexive. If in addition the dual spaces are locally reflexive and the bidual spaces have the completely bounded approximation property, then the identification is through a complete isomorphism. When α is the projective, Haagerup or injective norm, the hypotheses can be weakened.
Fil: Dimant, Veronica Isabel. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Fernández Unzueta, Maite. Centro de Investigación en Matemáticas; México
description We study whether the operator space V ∗∗ α ⊗ W∗∗ can be identified with a subspace of the bidual space (V α ⊗ W) ∗∗, for a given operator space tensor norm. We prove that this can be done if α is finitely generated and V and W are locally reflexive. If in addition the dual spaces are locally reflexive and the bidual spaces have the completely bounded approximation property, then the identification is through a complete isomorphism. When α is the projective, Haagerup or injective norm, the hypotheses can be weakened.
publishDate 2015
dc.date.none.fl_str_mv 2015-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/42352
Dimant, Veronica Isabel; Fernández Unzueta, Maite; Biduals of tensor products in operator spaces; Polish Academy of Sciences. Institute of Mathematics; Studia Mathematica; 230; 2; 12-2015; 165-185
0039-3223
CONICET Digital
CONICET
url http://hdl.handle.net/11336/42352
identifier_str_mv Dimant, Veronica Isabel; Fernández Unzueta, Maite; Biduals of tensor products in operator spaces; Polish Academy of Sciences. Institute of Mathematics; Studia Mathematica; 230; 2; 12-2015; 165-185
0039-3223
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8292-1-2016
info:eu-repo/semantics/altIdentifier/doi/10.4064/sm8292-1-2016
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Polish Academy of Sciences. Institute of Mathematics
publisher.none.fl_str_mv Polish Academy of Sciences. Institute of Mathematics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1844614513336254464
score 13.070432

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