Bounded holomorphic functions attaining their norms in the bidual

Under certain hypotheses on the Banach space X, we prove that the set of analytic functions in A<inf>u</inf>(X) (the algebra of all holomorphic and uniformly continuous functions in the ball of X) whose Aron-Berner extensions attain their norms is dense in A<inf>u</inf> (X)....

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Detalles Bibliográficos
Autor principal: Carando, Daniel German
Publicado: 2015
Materias:
Integral formula
Lindenstrauss type theorems
Norm attaining holomorphic mappings
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00345318_v51_n3_p489_Carando
http://hdl.handle.net/20.500.12110/paper_00345318_v51_n3_p489_Carando
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00345318_v51_n3_p489_Carando
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spelling paper:paper_00345318_v51_n3_p489_Carando2023-06-08T15:00:43Z Bounded holomorphic functions attaining their norms in the bidual Carando, Daniel German Integral formula Lindenstrauss type theorems Norm attaining holomorphic mappings Under certain hypotheses on the Banach space X, we prove that the set of analytic functions in A<inf>u</inf>(X) (the algebra of all holomorphic and uniformly continuous functions in the ball of X) whose Aron-Berner extensions attain their norms is dense in A<inf>u</inf> (X). This Lindenstrauss type result also holds for functions with values in a dual space or in a Banach space with the so-called property (β). We show that the Bishop-Phelps theorem does not hold for Au(co, Z") for a certain Banach space Z, while our Lindenstrauss theorem does. In order to obtain our results, we first handle their polynomial cases. © 2015 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved. Fil:Carando, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2015 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00345318_v51_n3_p489_Carando http://hdl.handle.net/20.500.12110/paper_00345318_v51_n3_p489_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 holomorphic mappings
spellingShingle Integral formula
Lindenstrauss type theorems
Norm attaining holomorphic mappings
Carando, Daniel German
Bounded holomorphic functions attaining their norms in the bidual
topic_facet Integral formula
Lindenstrauss type theorems
Norm attaining holomorphic mappings
description Under certain hypotheses on the Banach space X, we prove that the set of analytic functions in A<inf>u</inf>(X) (the algebra of all holomorphic and uniformly continuous functions in the ball of X) whose Aron-Berner extensions attain their norms is dense in A<inf>u</inf> (X). This Lindenstrauss type result also holds for functions with values in a dual space or in a Banach space with the so-called property (β). We show that the Bishop-Phelps theorem does not hold for Au(co, Z") for a certain Banach space Z, while our Lindenstrauss theorem does. In order to obtain our results, we first handle their polynomial cases. © 2015 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.
author Carando, Daniel German
author_facet Carando, Daniel German
author_sort Carando, Daniel German
title Bounded holomorphic functions attaining their norms in the bidual
title_short Bounded holomorphic functions attaining their norms in the bidual
title_full Bounded holomorphic functions attaining their norms in the bidual
title_fullStr Bounded holomorphic functions attaining their norms in the bidual
title_full_unstemmed Bounded holomorphic functions attaining their norms in the bidual
title_sort bounded holomorphic functions attaining their norms in the bidual
publishDate 2015
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00345318_v51_n3_p489_Carando
http://hdl.handle.net/20.500.12110/paper_00345318_v51_n3_p489_Carando
work_keys_str_mv AT carandodanielgerman boundedholomorphicfunctionsattainingtheirnormsinthebidual
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