Coincidence of extendible vector-valued ideals with their minimal kernel

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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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Autores principales: Galicer, D., Villafañe, R.
Formato: INPR
Materias:
Metric theory of tensor products
Multilinear mappings
Polynomial ideals
Radon-Nikodým property
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v_n_p_Galicer
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_0022247X_v_n_p_Galicer2023-10-03T14:29:28Z Coincidence of extendible vector-valued ideals with their minimal kernel Galicer, D. Villafañe, R. 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. INPR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, D.
Villafañe, R.
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.
format INPR
author Galicer, D.
Villafañe, R.
author_facet Galicer, D.
Villafañe, R.
author_sort Galicer, D.
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
url http://hdl.handle.net/20.500.12110/paper_0022247X_v_n_p_Galicer
work_keys_str_mv AT galicerd coincidenceofextendiblevectorvaluedidealswiththeirminimalkernel
AT villafaner coincidenceofextendiblevectorvaluedidealswiththeirminimalkernel
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