Bounded holomorphic functions attaining their norms in the bidual

Autores
Carando, Daniel Germán; Mazzitelli, Martin Diego
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Under certain hypotheses on the Banach space X, we prove that the set of analytic functions in Au(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 Au(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(c0, Z00) for a certain Banach space Z, while our Lindenstrauss theorem does. In order to obtain our results, we first handle their polynomial cases.
Fil: Carando, Daniel Germán. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Mazzitelli, Martin Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
Integral Formula
Norm Attaining Holomorphic Functions
Lindenstrauss-Type Theorems
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/18900
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Bounded holomorphic functions attaining their norms in the bidualCarando, Daniel GermánMazzitelli, Martin DiegoIntegral FormulaNorm Attaining Holomorphic FunctionsLindenstrauss-Type Theoremshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Under certain hypotheses on the Banach space X, we prove that the set of analytic functions in Au(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 Au(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(c0, Z00) for a certain Banach space Z, while our Lindenstrauss theorem does. In order to obtain our results, we first handle their polynomial cases.Fil: Carando, Daniel Germán. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Mazzitelli, Martin Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaKyoto Univ2015-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18900Carando, Daniel Germán; Mazzitelli, Martin Diego; Bounded holomorphic functions attaining their norms in the bidual; Kyoto Univ; Publications Of The Research Institute For Mathematical Sciences; 51; 3; 3-2015; 489-5120034-5318CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.4171/PRIMS/162info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=0034-5318&vol=51&iss=3&rank=3info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1403.6431info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:18:56Zoai:ri.conicet.gov.ar:11336/18900instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 12:18:56.849CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Bounded holomorphic functions attaining their norms in the bidual
title Bounded holomorphic functions attaining their norms in the bidual
spellingShingle Bounded holomorphic functions attaining their norms in the bidual
Carando, Daniel Germán
Integral Formula
Norm Attaining Holomorphic Functions
Lindenstrauss-Type Theorems
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
dc.creator.none.fl_str_mv Carando, Daniel Germán
Mazzitelli, Martin Diego
author Carando, Daniel Germán
author_facet Carando, Daniel Germán
Mazzitelli, Martin Diego
author_role author
author2 Mazzitelli, Martin Diego
author2_role author
dc.subject.none.fl_str_mv Integral Formula
Norm Attaining Holomorphic Functions
Lindenstrauss-Type Theorems
topic Integral Formula
Norm Attaining Holomorphic Functions
Lindenstrauss-Type Theorems
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Under certain hypotheses on the Banach space X, we prove that the set of analytic functions in Au(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 Au(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(c0, Z00) for a certain Banach space Z, while our Lindenstrauss theorem does. In order to obtain our results, we first handle their polynomial cases.
Fil: Carando, Daniel Germán. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Mazzitelli, Martin Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description Under certain hypotheses on the Banach space X, we prove that the set of analytic functions in Au(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 Au(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(c0, Z00) for a certain Banach space Z, while our Lindenstrauss theorem does. In order to obtain our results, we first handle their polynomial cases.
publishDate 2015
dc.date.none.fl_str_mv 2015-03
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/18900
Carando, Daniel Germán; Mazzitelli, Martin Diego; Bounded holomorphic functions attaining their norms in the bidual; Kyoto Univ; Publications Of The Research Institute For Mathematical Sciences; 51; 3; 3-2015; 489-512
0034-5318
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18900
identifier_str_mv Carando, Daniel Germán; Mazzitelli, Martin Diego; Bounded holomorphic functions attaining their norms in the bidual; Kyoto Univ; Publications Of The Research Institute For Mathematical Sciences; 51; 3; 3-2015; 489-512
0034-5318
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.4171/PRIMS/162
info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=0034-5318&vol=51&iss=3&rank=3
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1403.6431
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Kyoto Univ
publisher.none.fl_str_mv Kyoto Univ
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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