The symmetric Radon-Nikodỳm property for tensor norms

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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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Autores principales:	Carando, D., Galicer, D.
Formato:	Artículo publishedVersion
Publicado:	2011
Materias:	Metric theory of tensor products Polynomial ideals Radon-Nikodỳm property
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_0022247X_v375_n2_p553_Carando http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v375_n2_p553_Carando_oai
Aporte de:	Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires

id	I28-R145-paper_0022247X_v375_n2_p553_Carando_oai
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spelling	I28-R145-paper_0022247X_v375_n2_p553_Carando_oai2020-10-19 Carando, D. Galicer, D. 2011 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. application/pdf http://hdl.handle.net/20.500.12110/paper_0022247X_v375_n2_p553_Carando info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Math. Anal. Appl. 2011;375(2):553-565 Metric theory of tensor products Polynomial ideals Radon-Nikodỳm property The symmetric Radon-Nikodỳm property for tensor norms info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v375_n2_p553_Carando_oai
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-145
collection	Repositorio Digital de la Universidad de Buenos Aires (UBA)
topic	Metric theory of tensor products Polynomial ideals Radon-Nikodỳm property
spellingShingle	Metric theory of tensor products Polynomial ideals Radon-Nikodỳm property Carando, D. Galicer, D. 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.
format	Artículo Artículo publishedVersion
author	Carando, D. Galicer, D.
author_facet	Carando, D. Galicer, D.
author_sort	Carando, D.
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	http://hdl.handle.net/20.500.12110/paper_0022247X_v375_n2_p553_Carando http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v375_n2_p553_Carando_oai
work_keys_str_mv	AT carandod thesymmetricradonnikodympropertyfortensornorms AT galicerd thesymmetricradonnikodympropertyfortensornorms AT carandod symmetricradonnikodympropertyfortensornorms AT galicerd symmetricradonnikodympropertyfortensornorms
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The symmetric Radon-Nikodỳm property for tensor norms

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