Coincidence of extendible vector-valued ideals with their minimal kernel

We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if A is an ideal of n-linear mappings we give conditions for which the equality A(E1,. . .,En;F)=Amin(E1,. . .,En;F) holds isometrically. As an application, we obtain in many cases that the monomials fo...

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Detalles Bibliográficos
Publicado: 2015
Materias:
Metric theory of tensor products
Multilinear mappings
Polynomial ideals
Radon-Nikodým property
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v421_n2_p1743_Galicer
http://hdl.handle.net/20.500.12110/paper_0022247X_v421_n2_p1743_Galicer
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_0022247X_v421_n2_p1743_Galicer
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spelling paper:paper_0022247X_v421_n2_p1743_Galicer2023-06-08T14:47:58Z Coincidence of extendible vector-valued ideals with their minimal kernel Metric theory of tensor products Multilinear mappings Polynomial ideals Radon-Nikodým property We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if A is an ideal of n-linear mappings we give conditions for which the equality A(E1,. . .,En;F)=Amin(E1,. . .,En;F) holds isometrically. As an application, we obtain in many cases that the monomials form a Schauder basis of the space A(E1,. . .,En;F). Several structural and geometric properties are also derived using this equality. We apply our results to the particular case where A is the classical ideal of extendible or Pietsch-integral multilinear operators. Similar statements are given for ideals of vector-valued homogeneous polynomials. © 2014 Elsevier Inc. 2015 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v421_n2_p1743_Galicer http://hdl.handle.net/20.500.12110/paper_0022247X_v421_n2_p1743_Galicer
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
Multilinear mappings
Polynomial ideals
Radon-Nikodým property
spellingShingle Metric theory of tensor products
Multilinear mappings
Polynomial ideals
Radon-Nikodým property
Coincidence of extendible vector-valued ideals with their minimal kernel
topic_facet Metric theory of tensor products
Multilinear mappings
Polynomial ideals
Radon-Nikodým property
description We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if A is an ideal of n-linear mappings we give conditions for which the equality A(E1,. . .,En;F)=Amin(E1,. . .,En;F) holds isometrically. As an application, we obtain in many cases that the monomials form a Schauder basis of the space A(E1,. . .,En;F). Several structural and geometric properties are also derived using this equality. We apply our results to the particular case where A is the classical ideal of extendible or Pietsch-integral multilinear operators. Similar statements are given for ideals of vector-valued homogeneous polynomials. © 2014 Elsevier Inc.
title Coincidence of extendible vector-valued ideals with their minimal kernel
title_short Coincidence of extendible vector-valued ideals with their minimal kernel
title_full Coincidence of extendible vector-valued ideals with their minimal kernel
title_fullStr Coincidence of extendible vector-valued ideals with their minimal kernel
title_full_unstemmed Coincidence of extendible vector-valued ideals with their minimal kernel
title_sort coincidence of extendible vector-valued ideals with their minimal kernel
publishDate 2015
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v421_n2_p1743_Galicer
http://hdl.handle.net/20.500.12110/paper_0022247X_v421_n2_p1743_Galicer
_version_ 1768546332908191744

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