Fibers and Gleason parts for the maximal ideal space of Au(Bp )

Autores
Dimant, Veronica Isabel; Lassalle, Silvia Beatriz; Maestre, Manuel
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the early nineties, R. M. Aron, B. Cole, T. W. Gamelin and W. B. Johnson initiated the study of the maximal ideal space (spectrum) of Banach algebras of holomorphic functions defined on the open unit ball of an infinite dimensional complex Banach space. Within this framework, we investigate the fibers and Gleason parts of the spectrum of the algebra of holomorphic and uniformly continuous functions on the unit ball of p (1 ≤ p < ∞). We show that the inherent geometry of these spaces provides a fundamental ingredient for our results. We prove that whenever p ∈ N (p ≥ 2), the fiber of every z ∈ Bp contains a set of cardinal 2c such that any two elements of this set belong to different Gleason parts. For the case p = 1, we complete the known description of the fibers, showing that, for each z ∈ B 1 \S1 , the fiber over z is not a singleton. Also, we establish that different fibers over elements in S 1 cannot share Gleason parts.
Fil: Dimant, Veronica Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina
Fil: Lassalle, Silvia Beatriz. 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. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina
Fil: Maestre, Manuel. Universidad de Valencia; España
Materia
Algebras of holomorphic functions
Spectrum
Gleason parts
Fibers
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/265649
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Fibers and Gleason parts for the maximal ideal space of Au(Bp )Dimant, Veronica IsabelLassalle, Silvia BeatrizMaestre, ManuelAlgebras of holomorphic functionsSpectrumGleason partsFibershttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In the early nineties, R. M. Aron, B. Cole, T. W. Gamelin and W. B. Johnson initiated the study of the maximal ideal space (spectrum) of Banach algebras of holomorphic functions defined on the open unit ball of an infinite dimensional complex Banach space. Within this framework, we investigate the fibers and Gleason parts of the spectrum of the algebra of holomorphic and uniformly continuous functions on the unit ball of p (1 ≤ p < ∞). We show that the inherent geometry of these spaces provides a fundamental ingredient for our results. We prove that whenever p ∈ N (p ≥ 2), the fiber of every z ∈ Bp contains a set of cardinal 2c such that any two elements of this set belong to different Gleason parts. For the case p = 1, we complete the known description of the fibers, showing that, for each z ∈ B 1 \S1 , the fiber over z is not a singleton. Also, we establish that different fibers over elements in S 1 cannot share Gleason parts.Fil: Dimant, Veronica Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; ArgentinaFil: Lassalle, Silvia Beatriz. 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. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; ArgentinaFil: Maestre, Manuel. Universidad de Valencia; EspañaSpringer2025-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/265649Dimant, Veronica Isabel; Lassalle, Silvia Beatriz; Maestre, Manuel; Fibers and Gleason parts for the maximal ideal space of Au(Bp ); Springer; Banach Journal Of Mathematical Analysis; 19; 4; 1-2025; 1-211735-8787CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s43037-024-00388-0info:eu-repo/semantics/altIdentifier/doi/10.1007/s43037-024-00388-0info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:18:55Zoai:ri.conicet.gov.ar:11336/265649instacron: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:34982025-10-15 15:18:55.417CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Fibers and Gleason parts for the maximal ideal space of Au(Bp )
title Fibers and Gleason parts for the maximal ideal space of Au(Bp )
spellingShingle Fibers and Gleason parts for the maximal ideal space of Au(Bp )
Dimant, Veronica Isabel
Algebras of holomorphic functions
Spectrum
Gleason parts
Fibers
title_short Fibers and Gleason parts for the maximal ideal space of Au(Bp )
title_full Fibers and Gleason parts for the maximal ideal space of Au(Bp )
title_fullStr Fibers and Gleason parts for the maximal ideal space of Au(Bp )
title_full_unstemmed Fibers and Gleason parts for the maximal ideal space of Au(Bp )
title_sort Fibers and Gleason parts for the maximal ideal space of Au(Bp )
dc.creator.none.fl_str_mv Dimant, Veronica Isabel
Lassalle, Silvia Beatriz
Maestre, Manuel
author Dimant, Veronica Isabel
author_facet Dimant, Veronica Isabel
Lassalle, Silvia Beatriz
Maestre, Manuel
author_role author
author2 Lassalle, Silvia Beatriz
Maestre, Manuel
author2_role author
author
dc.subject.none.fl_str_mv Algebras of holomorphic functions
Spectrum
Gleason parts
Fibers
topic Algebras of holomorphic functions
Spectrum
Gleason parts
Fibers
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In the early nineties, R. M. Aron, B. Cole, T. W. Gamelin and W. B. Johnson initiated the study of the maximal ideal space (spectrum) of Banach algebras of holomorphic functions defined on the open unit ball of an infinite dimensional complex Banach space. Within this framework, we investigate the fibers and Gleason parts of the spectrum of the algebra of holomorphic and uniformly continuous functions on the unit ball of p (1 ≤ p < ∞). We show that the inherent geometry of these spaces provides a fundamental ingredient for our results. We prove that whenever p ∈ N (p ≥ 2), the fiber of every z ∈ Bp contains a set of cardinal 2c such that any two elements of this set belong to different Gleason parts. For the case p = 1, we complete the known description of the fibers, showing that, for each z ∈ B 1 \S1 , the fiber over z is not a singleton. Also, we establish that different fibers over elements in S 1 cannot share Gleason parts.
Fil: Dimant, Veronica Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina
Fil: Lassalle, Silvia Beatriz. 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. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina
Fil: Maestre, Manuel. Universidad de Valencia; España
description In the early nineties, R. M. Aron, B. Cole, T. W. Gamelin and W. B. Johnson initiated the study of the maximal ideal space (spectrum) of Banach algebras of holomorphic functions defined on the open unit ball of an infinite dimensional complex Banach space. Within this framework, we investigate the fibers and Gleason parts of the spectrum of the algebra of holomorphic and uniformly continuous functions on the unit ball of p (1 ≤ p < ∞). We show that the inherent geometry of these spaces provides a fundamental ingredient for our results. We prove that whenever p ∈ N (p ≥ 2), the fiber of every z ∈ Bp contains a set of cardinal 2c such that any two elements of this set belong to different Gleason parts. For the case p = 1, we complete the known description of the fibers, showing that, for each z ∈ B 1 \S1 , the fiber over z is not a singleton. Also, we establish that different fibers over elements in S 1 cannot share Gleason parts.
publishDate 2025
dc.date.none.fl_str_mv 2025-01
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/11336/265649
Dimant, Veronica Isabel; Lassalle, Silvia Beatriz; Maestre, Manuel; Fibers and Gleason parts for the maximal ideal space of Au(Bp ); Springer; Banach Journal Of Mathematical Analysis; 19; 4; 1-2025; 1-21
1735-8787
CONICET Digital
CONICET
url http://hdl.handle.net/11336/265649
identifier_str_mv Dimant, Veronica Isabel; Lassalle, Silvia Beatriz; Maestre, Manuel; Fibers and Gleason parts for the maximal ideal space of Au(Bp ); Springer; Banach Journal Of Mathematical Analysis; 19; 4; 1-2025; 1-21
1735-8787
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s43037-024-00388-0
info:eu-repo/semantics/altIdentifier/doi/10.1007/s43037-024-00388-0
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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 13.22299

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