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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Autores principales: Carando, Daniel German, Lassalle, Silvia Beatriz
Publicado: 2008
Materias:
Atomic decompositions
Homogeneous polynomials
Polynomial ideals
Symmetric tensor norms
Tensor products
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v347_n1_p243_Carando
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 paper:paper_0022247X_v347_n1_p243_Carando
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spelling paper:paper_0022247X_v347_n1_p243_Carando2023-06-08T14:47:52Z Atomic decompositions for tensor products and polynomial spaces Carando, Daniel German Lassalle, Silvia Beatriz 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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v347_n1_p243_Carando 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)
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, Daniel German
Lassalle, Silvia Beatriz
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.
author Carando, Daniel German
Lassalle, Silvia Beatriz
author_facet Carando, Daniel German
Lassalle, Silvia Beatriz
author_sort Carando, Daniel German
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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v347_n1_p243_Carando
http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p243_Carando
work_keys_str_mv AT carandodanielgerman atomicdecompositionsfortensorproductsandpolynomialspaces
AT lassallesilviabeatriz atomicdecompositionsfortensorproductsandpolynomialspaces
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