Cluster values for algebras of analytic functions

Autores
Carando, Daniel Germán; Galicer, Daniel Eric; Muro, Luis Santiago Miguel; Sevilla Peris, Pablo
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The Cluster Value Theorem is known for being a weak version of the classical Corona Theorem. Given a Banach space X, we study the Cluster Value Problem for the ball algebra Au(BX), the Banach algebra of all uniformly continuous holomorphic functions on the unit ball BX; and also for the Fréchet algebra Hb(X) of holomorphic functions of bounded type on X (more generally, for Hb(U), the algebra of holomorphic functions of bounded type on a given balanced open subset U⊂X). We show that Cluster Value Theorems hold for all of these algebras whenever the dual of X has the bounded approximation property. These results are an important advance in this problem, since the validity of these theorems was known only for trivial cases (where the spectrum is formed only by evaluation functionals) and for the infinite dimensional Hilbert space. As a consequence, we obtain weak analytic Nullstellensatz theorems and several structural results for the spectrum of these algebras.
Fil: Carando, Daniel. Universidad de Buenos Aires; Argentina
Fil: Galicer, Daniel. Universidad de Buenos Aires; Argentina
Fil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
Fil: Sevilla-Peris, Pablo. Universidad Politécnica de Valencia; España
Materia
ANALYTIC FUNCTIONS OF BOUNDED TYPE
BALL ALGEBRA
CLUSTER VALUE PROBLEM
CORONA THEOREM
FIBER
SPECTRUM
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/92695
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/92695
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Cluster values for algebras of analytic functionsCarando, Daniel GermánGalicer, Daniel EricMuro, Luis Santiago MiguelSevilla Peris, PabloANALYTIC FUNCTIONS OF BOUNDED TYPEBALL ALGEBRACLUSTER VALUE PROBLEMCORONA THEOREMFIBERSPECTRUMhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The Cluster Value Theorem is known for being a weak version of the classical Corona Theorem. Given a Banach space X, we study the Cluster Value Problem for the ball algebra Au(BX), the Banach algebra of all uniformly continuous holomorphic functions on the unit ball BX; and also for the Fréchet algebra Hb(X) of holomorphic functions of bounded type on X (more generally, for Hb(U), the algebra of holomorphic functions of bounded type on a given balanced open subset U⊂X). We show that Cluster Value Theorems hold for all of these algebras whenever the dual of X has the bounded approximation property. These results are an important advance in this problem, since the validity of these theorems was known only for trivial cases (where the spectrum is formed only by evaluation functionals) and for the infinite dimensional Hilbert space. As a consequence, we obtain weak analytic Nullstellensatz theorems and several structural results for the spectrum of these algebras.Fil: Carando, Daniel. Universidad de Buenos Aires; ArgentinaFil: Galicer, Daniel. Universidad de Buenos Aires; ArgentinaFil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: Sevilla-Peris, Pablo. Universidad Politécnica de Valencia; EspañaAcademic Press Inc Elsevier Science2018-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/92695Carando, Daniel Germán; Galicer, Daniel Eric; Muro, Luis Santiago Miguel; Sevilla Peris, Pablo; Cluster values for algebras of analytic functions; Academic Press Inc Elsevier Science; Advances in Mathematics; 329; 4-2018; 157-1730001-8708CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2017.08.030info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0001870816312075info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1705.05697info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:25:15Zoai:ri.conicet.gov.ar:11336/92695instacron: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 11:25:15.295CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Cluster values for algebras of analytic functions
title Cluster values for algebras of analytic functions
spellingShingle Cluster values for algebras of analytic functions
Carando, Daniel Germán
ANALYTIC FUNCTIONS OF BOUNDED TYPE
BALL ALGEBRA
CLUSTER VALUE PROBLEM
CORONA THEOREM
FIBER
SPECTRUM
title_short Cluster values for algebras of analytic functions
title_full Cluster values for algebras of analytic functions
title_fullStr Cluster values for algebras of analytic functions
title_full_unstemmed Cluster values for algebras of analytic functions
title_sort Cluster values for algebras of analytic functions
dc.creator.none.fl_str_mv Carando, Daniel Germán
Galicer, Daniel Eric
Muro, Luis Santiago Miguel
Sevilla Peris, Pablo
author Carando, Daniel Germán
author_facet Carando, Daniel Germán
Galicer, Daniel Eric
Muro, Luis Santiago Miguel
Sevilla Peris, Pablo
author_role author
author2 Galicer, Daniel Eric
Muro, Luis Santiago Miguel
Sevilla Peris, Pablo
author2_role author
author
author
dc.subject.none.fl_str_mv ANALYTIC FUNCTIONS OF BOUNDED TYPE
BALL ALGEBRA
CLUSTER VALUE PROBLEM
CORONA THEOREM
FIBER
SPECTRUM
topic ANALYTIC FUNCTIONS OF BOUNDED TYPE
BALL ALGEBRA
CLUSTER VALUE PROBLEM
CORONA THEOREM
FIBER
SPECTRUM
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The Cluster Value Theorem is known for being a weak version of the classical Corona Theorem. Given a Banach space X, we study the Cluster Value Problem for the ball algebra Au(BX), the Banach algebra of all uniformly continuous holomorphic functions on the unit ball BX; and also for the Fréchet algebra Hb(X) of holomorphic functions of bounded type on X (more generally, for Hb(U), the algebra of holomorphic functions of bounded type on a given balanced open subset U⊂X). We show that Cluster Value Theorems hold for all of these algebras whenever the dual of X has the bounded approximation property. These results are an important advance in this problem, since the validity of these theorems was known only for trivial cases (where the spectrum is formed only by evaluation functionals) and for the infinite dimensional Hilbert space. As a consequence, we obtain weak analytic Nullstellensatz theorems and several structural results for the spectrum of these algebras.
Fil: Carando, Daniel. Universidad de Buenos Aires; Argentina
Fil: Galicer, Daniel. Universidad de Buenos Aires; Argentina
Fil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
Fil: Sevilla-Peris, Pablo. Universidad Politécnica de Valencia; España
description The Cluster Value Theorem is known for being a weak version of the classical Corona Theorem. Given a Banach space X, we study the Cluster Value Problem for the ball algebra Au(BX), the Banach algebra of all uniformly continuous holomorphic functions on the unit ball BX; and also for the Fréchet algebra Hb(X) of holomorphic functions of bounded type on X (more generally, for Hb(U), the algebra of holomorphic functions of bounded type on a given balanced open subset U⊂X). We show that Cluster Value Theorems hold for all of these algebras whenever the dual of X has the bounded approximation property. These results are an important advance in this problem, since the validity of these theorems was known only for trivial cases (where the spectrum is formed only by evaluation functionals) and for the infinite dimensional Hilbert space. As a consequence, we obtain weak analytic Nullstellensatz theorems and several structural results for the spectrum of these algebras.
publishDate 2018
dc.date.none.fl_str_mv 2018-04
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/11336/92695
Carando, Daniel Germán; Galicer, Daniel Eric; Muro, Luis Santiago Miguel; Sevilla Peris, Pablo; Cluster values for algebras of analytic functions; Academic Press Inc Elsevier Science; Advances in Mathematics; 329; 4-2018; 157-173
0001-8708
CONICET Digital
CONICET
url http://hdl.handle.net/11336/92695
identifier_str_mv Carando, Daniel Germán; Galicer, Daniel Eric; Muro, Luis Santiago Miguel; Sevilla Peris, Pablo; Cluster values for algebras of analytic functions; Academic Press Inc Elsevier Science; Advances in Mathematics; 329; 4-2018; 157-173
0001-8708
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2017.08.030
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0001870816312075
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1705.05697
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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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