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 mono...

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Autor principal: Galicer, Daniel Eric
Publicado: 2014
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_v_n_p_Galicer
http://hdl.handle.net/20.500.12110/paper_0022247X_v_n_p_Galicer
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_0022247X_v_n_p_Galicer2023-06-08T14:48:03Z Coincidence of extendible vector-valued ideals with their minimal kernel Galicer, Daniel Eric 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. All rights reserved. Fil:Galicer, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v_n_p_Galicer http://hdl.handle.net/20.500.12110/paper_0022247X_v_n_p_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
Galicer, Daniel Eric
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. All rights reserved.
author Galicer, Daniel Eric
author_facet Galicer, Daniel Eric
author_sort Galicer, Daniel Eric
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 2014
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v_n_p_Galicer
http://hdl.handle.net/20.500.12110/paper_0022247X_v_n_p_Galicer
work_keys_str_mv AT galicerdanieleric coincidenceofextendiblevectorvaluedidealswiththeirminimalkernel
_version_ 1768542773476065280

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