A Lindenstrauss theorem for some classes of multilinear mappings

Under some natural hypotheses, we show that if a multilinear mapping belongs to some Banach multilinear ideal, then it can be approximated by multilinear mappings belonging to the same ideal all whose Arens extensions attain their norms at the same point. We prove a similar result for the class of s...

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Autores principales: Carando, D., Lassalle, S., Mazzitelli, M.
Formato: JOUR
Materias:
Integral formula
Lindenstrauss-type theorems
Norm attaining multilinear mappings and polynomials
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v427_n1_p248_Carando
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_0022247X_v427_n1_p248_Carando
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spelling todo:paper_0022247X_v427_n1_p248_Carando2023-10-03T14:29:21Z A Lindenstrauss theorem for some classes of multilinear mappings Carando, D. Lassalle, S. Mazzitelli, M. Integral formula Lindenstrauss-type theorems Norm attaining multilinear mappings and polynomials Under some natural hypotheses, we show that if a multilinear mapping belongs to some Banach multilinear ideal, then it can be approximated by multilinear mappings belonging to the same ideal all whose Arens extensions attain their norms at the same point. We prove a similar result for the class of symmetric multilinear mappings. We see that the quantitative (Bollobás-type) version of these results fails in every multilinear ideal. © 2014. Fil:Carando, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Lassalle, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0022247X_v427_n1_p248_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 Integral formula
Lindenstrauss-type theorems
Norm attaining multilinear mappings and polynomials
spellingShingle Integral formula
Lindenstrauss-type theorems
Norm attaining multilinear mappings and polynomials
Carando, D.
Lassalle, S.
Mazzitelli, M.
A Lindenstrauss theorem for some classes of multilinear mappings
topic_facet Integral formula
Lindenstrauss-type theorems
Norm attaining multilinear mappings and polynomials
description Under some natural hypotheses, we show that if a multilinear mapping belongs to some Banach multilinear ideal, then it can be approximated by multilinear mappings belonging to the same ideal all whose Arens extensions attain their norms at the same point. We prove a similar result for the class of symmetric multilinear mappings. We see that the quantitative (Bollobás-type) version of these results fails in every multilinear ideal. © 2014.
format JOUR
author Carando, D.
Lassalle, S.
Mazzitelli, M.
author_facet Carando, D.
Lassalle, S.
Mazzitelli, M.
author_sort Carando, D.
title A Lindenstrauss theorem for some classes of multilinear mappings
title_short A Lindenstrauss theorem for some classes of multilinear mappings
title_full A Lindenstrauss theorem for some classes of multilinear mappings
title_fullStr A Lindenstrauss theorem for some classes of multilinear mappings
title_full_unstemmed A Lindenstrauss theorem for some classes of multilinear mappings
title_sort lindenstrauss theorem for some classes of multilinear mappings
url http://hdl.handle.net/20.500.12110/paper_0022247X_v427_n1_p248_Carando
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AT mazzitellim alindenstrausstheoremforsomeclassesofmultilinearmappings
AT carandod lindenstrausstheoremforsomeclassesofmultilinearmappings
AT lassalles lindenstrausstheoremforsomeclassesofmultilinearmappings
AT mazzitellim lindenstrausstheoremforsomeclassesofmultilinearmappings
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