The symmetric Radon-Nikodým property for tensor norms

Autores
Carando, Daniel Germán; Galicer, Daniel Eric
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We introduce the symmetric-Radon-Nikodým property (sRN pr operty) for finitely generated s-tensor norms β of order n and prove a Lewis type theorem for s-tensor norms with this property. As a consequence, if β is a projective s-tensor norm with the sRN prop- erty, then for every Asplund space E , the canonical map e ⊗ n,s β E ′ → e ⊗ n,s β ′ E ′ is a metric surjection. This can be rephrased as the isometric isomorph ism Q min ( E ) = Q ( E ) for certain polynomial ideal Q . We also relate the sRN property of an s-tensor norm with the A splund or Radon-Nikodým properties of different tensor products. S imilar results for full tensor products are also given. As an application, results concern ing the ideal of n -homogeneous extendible polynomials are obtained, as well as a new proof o f the well known isometric isomorphism between nuclear and integral polynomials on As plund spaces.
Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Galicer, Daniel Eric. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
Polynomial ideals
Symmetric tensor products of Banach spaces
Radon-Nikodým property
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:11336/14933
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The symmetric Radon-Nikodým property for tensor normsCarando, Daniel GermánGalicer, Daniel EricPolynomial idealsSymmetric tensor products of Banach spacesRadon-Nikodým propertyhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We introduce the symmetric-Radon-Nikodým property (sRN pr operty) for finitely generated s-tensor norms β of order n and prove a Lewis type theorem for s-tensor norms with this property. As a consequence, if β is a projective s-tensor norm with the sRN prop- erty, then for every Asplund space E , the canonical map e ⊗ n,s β E ′ → e ⊗ n,s β ′ E ′ is a metric surjection. This can be rephrased as the isometric isomorph ism Q min ( E ) = Q ( E ) for certain polynomial ideal Q . We also relate the sRN property of an s-tensor norm with the A splund or Radon-Nikodým properties of different tensor products. S imilar results for full tensor products are also given. As an application, results concern ing the ideal of n -homogeneous extendible polynomials are obtained, as well as a new proof o f the well known isometric isomorphism between nuclear and integral polynomials on As plund spaces.Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Galicer, Daniel Eric. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaElsevier2010-09-29info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14933Carando, Daniel Germán; Galicer, Daniel Eric; The symmetric Radon-Nikodým property for tensor norms; Elsevier; Journal Of Mathematical Analysis And Applications; 375; 2; 29-9-2010; 553-5650022-247Xenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022247X10008012info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2010.09.044info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:14:45Zoai:ri.conicet.gov.ar:11336/14933instacron: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:34982025-10-15 15:14:46.169CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The symmetric Radon-Nikodým property for tensor norms
title The symmetric Radon-Nikodým property for tensor norms
spellingShingle The symmetric Radon-Nikodým property for tensor norms
Carando, Daniel Germán
Polynomial ideals
Symmetric tensor products of Banach spaces
Radon-Nikodým property
title_short The symmetric Radon-Nikodým property for tensor norms
title_full The symmetric Radon-Nikodým property for tensor norms
title_fullStr The symmetric Radon-Nikodým property for tensor norms
title_full_unstemmed The symmetric Radon-Nikodým property for tensor norms
title_sort The symmetric Radon-Nikodým property for tensor norms
dc.creator.none.fl_str_mv Carando, Daniel Germán
Galicer, Daniel Eric
author Carando, Daniel Germán
author_facet Carando, Daniel Germán
Galicer, Daniel Eric
author_role author
author2 Galicer, Daniel Eric
author2_role author
dc.subject.none.fl_str_mv Polynomial ideals
Symmetric tensor products of Banach spaces
Radon-Nikodým property
topic Polynomial ideals
Symmetric tensor products of Banach spaces
Radon-Nikodým property
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 introduce the symmetric-Radon-Nikodým property (sRN pr operty) for finitely generated s-tensor norms β of order n and prove a Lewis type theorem for s-tensor norms with this property. As a consequence, if β is a projective s-tensor norm with the sRN prop- erty, then for every Asplund space E , the canonical map e ⊗ n,s β E ′ → e ⊗ n,s β ′ E ′ is a metric surjection. This can be rephrased as the isometric isomorph ism Q min ( E ) = Q ( E ) for certain polynomial ideal Q . We also relate the sRN property of an s-tensor norm with the A splund or Radon-Nikodým properties of different tensor products. S imilar results for full tensor products are also given. As an application, results concern ing the ideal of n -homogeneous extendible polynomials are obtained, as well as a new proof o f the well known isometric isomorphism between nuclear and integral polynomials on As plund spaces.
Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Galicer, Daniel Eric. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We introduce the symmetric-Radon-Nikodým property (sRN pr operty) for finitely generated s-tensor norms β of order n and prove a Lewis type theorem for s-tensor norms with this property. As a consequence, if β is a projective s-tensor norm with the sRN prop- erty, then for every Asplund space E , the canonical map e ⊗ n,s β E ′ → e ⊗ n,s β ′ E ′ is a metric surjection. This can be rephrased as the isometric isomorph ism Q min ( E ) = Q ( E ) for certain polynomial ideal Q . We also relate the sRN property of an s-tensor norm with the A splund or Radon-Nikodým properties of different tensor products. S imilar results for full tensor products are also given. As an application, results concern ing the ideal of n -homogeneous extendible polynomials are obtained, as well as a new proof o f the well known isometric isomorphism between nuclear and integral polynomials on As plund spaces.
publishDate 2010
dc.date.none.fl_str_mv 2010-09-29
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/11336/14933
Carando, Daniel Germán; Galicer, Daniel Eric; The symmetric Radon-Nikodým property for tensor norms; Elsevier; Journal Of Mathematical Analysis And Applications; 375; 2; 29-9-2010; 553-565
0022-247X
url http://hdl.handle.net/11336/14933
identifier_str_mv Carando, Daniel Germán; Galicer, Daniel Eric; The symmetric Radon-Nikodým property for tensor norms; Elsevier; Journal Of Mathematical Analysis And Applications; 375; 2; 29-9-2010; 553-565
0022-247X
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022247X10008012
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2010.09.044
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
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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
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score 13.22299

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