On the polynomial lindenstrauss theorem

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Under certain hypotheses on the Banach space X, we show that the set of N-homogeneous polynomials from X to any dual space, whose Aron-Berner extensions are norm attaining, is dense in the space of all continuous N-homogeneous polynomials. To this end we prove an integral formula for the duality bet...

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Detalles Bibliográficos
Autores principales: Carando, D., Lassalle, S., Mazzitelli, M.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2012
Materias:
Integral formula
Lindenstrauss type theorems
Norm attaining multilinear and polynomials mappings
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00221236_v263_n7_p1809_Carando
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paperaa:paper_00221236_v263_n7_p1809_Carando2023-06-12T16:43:53Z On the polynomial lindenstrauss theorem J. Funct. Anal. 2012;263(7):1809-1824 Carando, D. Lassalle, S. Mazzitelli, M. Integral formula Lindenstrauss type theorems Norm attaining multilinear and polynomials mappings Under certain hypotheses on the Banach space X, we show that the set of N-homogeneous polynomials from X to any dual space, whose Aron-Berner extensions are norm attaining, is dense in the space of all continuous N-homogeneous polynomials. To this end we prove an integral formula for the duality between tensor products and polynomials. We also exhibit examples of Lorentz sequence spaces for which there is no polynomial Bishop-Phelps theorem, but our results apply. Finally we address quantitative versions, in the sense of Bollobás, of these results. © 2012 Elsevier Inc.. 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. 2012 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00221236_v263_n7_p1809_Carando
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Integral formula
Lindenstrauss type theorems
Norm attaining multilinear and polynomials mappings
spellingShingle Integral formula
Lindenstrauss type theorems
Norm attaining multilinear and polynomials mappings
Carando, D.
Lassalle, S.
Mazzitelli, M.
On the polynomial lindenstrauss theorem
topic_facet Integral formula
Lindenstrauss type theorems
Norm attaining multilinear and polynomials mappings
description Under certain hypotheses on the Banach space X, we show that the set of N-homogeneous polynomials from X to any dual space, whose Aron-Berner extensions are norm attaining, is dense in the space of all continuous N-homogeneous polynomials. To this end we prove an integral formula for the duality between tensor products and polynomials. We also exhibit examples of Lorentz sequence spaces for which there is no polynomial Bishop-Phelps theorem, but our results apply. Finally we address quantitative versions, in the sense of Bollobás, of these results. © 2012 Elsevier Inc..
format Artículo
Artículo
publishedVersion
author Carando, D.
Lassalle, S.
Mazzitelli, M.
author_facet Carando, D.
Lassalle, S.
Mazzitelli, M.
author_sort Carando, D.
title On the polynomial lindenstrauss theorem
title_short On the polynomial lindenstrauss theorem
title_full On the polynomial lindenstrauss theorem
title_fullStr On the polynomial lindenstrauss theorem
title_full_unstemmed On the polynomial lindenstrauss theorem
title_sort on the polynomial lindenstrauss theorem
publishDate 2012
url http://hdl.handle.net/20.500.12110/paper_00221236_v263_n7_p1809_Carando
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AT mazzitellim onthepolynomiallindenstrausstheorem
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