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Atomic decompositions for tensor products and polynomial spaces

Carando, D. - Lassalle, S.

Fecha:

2008

Tipo de documento:

info:eu-repo/semantics/article
info:ar-repo/semantics/artículo
info:eu-repo/semantics/publishedVersion

Formato:

application/pdf

Temas:

Atomic decompositions - Homogeneous polynomials - Polynomial ideals - Symmetric tensor norms - Tensor products

Descripción:

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.

Fuente:

J. Math. Anal. Appl. 2008;347(1):243-254

Identificador:

http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p243_Carando
http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v347_n1_p243_Carando_oai

Derechos:

info:eu-repo/semantics/openAccess

Cita bibliográfica:

Carando, D. ; Lassalle, S. (2008). Atomic decompositions for tensor products and polynomial spaces. (info:eu-repo/semantics/article). [consultado: ] Disponible en el Repositorio Digital Institucional de la Universidad de Buenos Aires: <http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p243_Carando>