The symmetric Radon-Nikodỳm property for tensor norms

We introduce the symmetric Radon-Nikodỳm property (sRN property) 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 property, then for every Asplund space E, the ca...

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Detalles Bibliográficos
Autores principales: Carando, Daniel German, Galicer, Daniel Eric
Publicado: 2011
Materias:
Metric theory of tensor products
Polynomial ideals
Radon-Nikodỳm property
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v375_n2_p553_Carando
http://hdl.handle.net/20.500.12110/paper_0022247X_v375_n2_p553_Carando
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_0022247X_v375_n2_p553_Carando
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spelling paper:paper_0022247X_v375_n2_p553_Carando2023-06-08T14:47:54Z The symmetric Radon-Nikodỳm property for tensor norms Carando, Daniel German Galicer, Daniel Eric Metric theory of tensor products Polynomial ideals Radon-Nikodỳm property We introduce the symmetric Radon-Nikodỳm property (sRN property) 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 property, then for every Asplund space E, the canonical mapping {position indicator}~βn,sE'→({position indicator}~β'n,sE)' is a metric surjection. This can be rephrased as the isometric isomorphism Qmin(E)=Q(E) for some polynomial ideal Q. We also relate the sRN property of an s-tensor norm with the Asplund or Radon-Nikodỳm properties of different tensor products. As an application, results concerning the ideal of n-homogeneous extendible polynomials are obtained, as well as a new proof of the well-known isometric isomorphism between nuclear and integral polynomials on Asplund spaces. An analogous study is carried out for full tensor products. © 2010 Elsevier Inc. Fil:Carando, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Galicer, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v375_n2_p553_Carando http://hdl.handle.net/20.500.12110/paper_0022247X_v375_n2_p553_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 Metric theory of tensor products
Polynomial ideals
Radon-Nikodỳm property
spellingShingle Metric theory of tensor products
Polynomial ideals
Radon-Nikodỳm property
Carando, Daniel German
Galicer, Daniel Eric
The symmetric Radon-Nikodỳm property for tensor norms
topic_facet Metric theory of tensor products
Polynomial ideals
Radon-Nikodỳm property
description We introduce the symmetric Radon-Nikodỳm property (sRN property) 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 property, then for every Asplund space E, the canonical mapping {position indicator}~βn,sE'→({position indicator}~β'n,sE)' is a metric surjection. This can be rephrased as the isometric isomorphism Qmin(E)=Q(E) for some polynomial ideal Q. We also relate the sRN property of an s-tensor norm with the Asplund or Radon-Nikodỳm properties of different tensor products. As an application, results concerning the ideal of n-homogeneous extendible polynomials are obtained, as well as a new proof of the well-known isometric isomorphism between nuclear and integral polynomials on Asplund spaces. An analogous study is carried out for full tensor products. © 2010 Elsevier Inc.
author Carando, Daniel German
Galicer, Daniel Eric
author_facet Carando, Daniel German
Galicer, Daniel Eric
author_sort Carando, Daniel German
title The symmetric Radon-Nikodỳm property for tensor norms
title_short The symmetric Radon-Nikodỳm property for tensor norms
title_full The symmetric Radon-Nikodỳm property for tensor norms
title_fullStr The symmetric Radon-Nikodỳm property for tensor norms
title_full_unstemmed The symmetric Radon-Nikodỳm property for tensor norms
title_sort symmetric radon-nikodỳm property for tensor norms
publishDate 2011
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v375_n2_p553_Carando
http://hdl.handle.net/20.500.12110/paper_0022247X_v375_n2_p553_Carando
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AT galicerdanieleric thesymmetricradonnikodympropertyfortensornorms
AT carandodanielgerman symmetricradonnikodympropertyfortensornorms
AT galicerdanieleric symmetricradonnikodympropertyfortensornorms
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