Atomic decompositions for tensor products and polynomial spaces

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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 principales: Carando, D., Lassalle, S.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2008
Materias:
Atomic decompositions
Homogeneous polynomials
Polynomial ideals
Symmetric tensor norms
Tensor products
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p243_Carando
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paperaa:paper_0022247X_v347_n1_p243_Carando
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spelling paperaa:paper_0022247X_v347_n1_p243_Carando2023-06-12T16:44:09Z Atomic decompositions for tensor products and polynomial spaces J. Math. Anal. Appl. 2008;347(1):243-254 Carando, D. Lassalle, S. Atomic decompositions Homogeneous polynomials Polynomial ideals Symmetric tensor norms Tensor products 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. 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. 2008 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p243_Carando
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Atomic decompositions
Homogeneous polynomials
Polynomial ideals
Symmetric tensor norms
Tensor products
spellingShingle Atomic decompositions
Homogeneous polynomials
Polynomial ideals
Symmetric tensor norms
Tensor products
Carando, D.
Lassalle, S.
Atomic decompositions for tensor products and polynomial spaces
topic_facet 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.
format Artículo
Artículo
publishedVersion
author Carando, D.
Lassalle, S.
author_facet Carando, D.
Lassalle, S.
author_sort Carando, D.
title Atomic decompositions for tensor products and polynomial spaces
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
publishDate 2008
url http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p243_Carando
work_keys_str_mv AT carandod atomicdecompositionsfortensorproductsandpolynomialspaces
AT lassalles atomicdecompositionsfortensorproductsandpolynomialspaces
_version_ 1769810091097194496

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