Atomic decompositions for tensor products and polynomial spaces

We study the existence of atomic decompositions for tensor products of Banach spaces and spaces of homogeneous polynomials. If a Banach space X admits an atomic decomposition of a certain kind, we show that the symmetrized tensor product of the elements of the atomic decomposition provides an atomic...

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Detalles Bibliográficos
Autores: Carando, D., Lassalle, S.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2008
País:Argentina
Institución:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
Repositorio:Biblioteca Digital (UBA-FCEN)
Idioma:inglés
OAI Identifier:paperaa:paper_0022247X_v347_n1_p243_Carando
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p243_Carando
Access Level:acceso abierto
Palabra clave:Atomic decompositions
Homogeneous polynomials
Polynomial ideals
Symmetric tensor norms
Tensor products
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spelling Atomic decompositions for tensor products and polynomial spacesCarando, D.Lassalle, S.Atomic decompositionsHomogeneous polynomialsPolynomial idealsSymmetric tensor normsTensor productsWe study the existence of atomic decompositions for tensor products of Banach spaces and spaces of homogeneous polynomials. If a Banach space X admits an atomic decomposition of a certain kind, we show that the symmetrized tensor product of the elements of the atomic decomposition provides an atomic decomposition for the symmetric tensor product ⊗s, μ n X, for any symmetric tensor norm μ. In addition, the reciprocal statement is investigated and analogous consequences for the full tensor product are obtained. Finally we apply the previous results to establish the existence of monomial atomic decompositions for certain ideals of polynomials on X. © 2008 Elsevier Inc. All rights reserved.Fil:Carando, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Lassalle, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2008info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p243_CarandoJ. Math. Anal. Appl. 2008;347(1):243-254reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2024-05-10T10:42:36Zpaperaa:paper_0022247X_v347_n1_p243_CarandoInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962024-05-10 10:42:37.4Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv Atomic decompositions for tensor products and polynomial spaces
title Atomic decompositions for tensor products and polynomial spaces
spellingShingle Atomic decompositions for tensor products and polynomial spaces
Carando, D.
Atomic decompositions
Homogeneous polynomials
Polynomial ideals
Symmetric tensor norms
Tensor products
title_short Atomic decompositions for tensor products and polynomial spaces
title_full Atomic decompositions for tensor products and polynomial spaces
title_fullStr Atomic decompositions for tensor products and polynomial spaces
title_full_unstemmed Atomic decompositions for tensor products and polynomial spaces
title_sort Atomic decompositions for tensor products and polynomial spaces
dc.creator.none.fl_str_mv Carando, D.
Lassalle, S.
author Carando, D.
author_facet Carando, D.
Lassalle, S.
author_role author
author2 Lassalle, S.
author2_role author
dc.subject.none.fl_str_mv Atomic decompositions
Homogeneous polynomials
Polynomial ideals
Symmetric tensor norms
Tensor products
topic Atomic decompositions
Homogeneous polynomials
Polynomial ideals
Symmetric tensor norms
Tensor products
description We study the existence of atomic decompositions for tensor products of Banach spaces and spaces of homogeneous polynomials. If a Banach space X admits an atomic decomposition of a certain kind, we show that the symmetrized tensor product of the elements of the atomic decomposition provides an atomic decomposition for the symmetric tensor product ⊗s, μ n X, for any symmetric tensor norm μ. In addition, the reciprocal statement is investigated and analogous consequences for the full tensor product are obtained. Finally we apply the previous results to establish the existence of monomial atomic decompositions for certain ideals of polynomials on X. © 2008 Elsevier Inc. All rights reserved.
publishDate 2008
dc.date.none.fl_str_mv 2008
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/20.500.12110/paper_0022247X_v347_n1_p243_Carando
url http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p243_Carando
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv J. Math. Anal. Appl. 2008;347(1):243-254
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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