Cluster values of holomorphic functions of bounded type

We study the cluster value theorem for Hb(X), the Fréchet algebra of holomorphic functions bounded on bounded sets of X. We also describe the (size of) fibers of the spectrum of Hb(X). Our results are rather complete whenever X has an unconditional shrinking basis and for X = ℓ1. As a byproduct, we...

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Autores principales: Carando, Daniel German, Lassalle, Silvia Beatriz
Publicado: 2016
Materias:
Analytic functions of bounded type
Banach space
Cluster value
Fiber
Spectrum
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029947_v368_n4_p2355_Aron
http://hdl.handle.net/20.500.12110/paper_00029947_v368_n4_p2355_Aron
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00029947_v368_n4_p2355_Aron
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spelling paper:paper_00029947_v368_n4_p2355_Aron2023-06-08T14:23:40Z Cluster values of holomorphic functions of bounded type Carando, Daniel German Lassalle, Silvia Beatriz Analytic functions of bounded type Banach space Cluster value Fiber Spectrum We study the cluster value theorem for Hb(X), the Fréchet algebra of holomorphic functions bounded on bounded sets of X. We also describe the (size of) fibers of the spectrum of Hb(X). Our results are rather complete whenever X has an unconditional shrinking basis and for X = ℓ1. As a byproduct, we obtain results on the spectrum of the algebra of all uniformly continuous holomorphic functions on the ball of ℓ1. © 2015 American Mathematical Society. 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. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029947_v368_n4_p2355_Aron http://hdl.handle.net/20.500.12110/paper_00029947_v368_n4_p2355_Aron
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Analytic functions of bounded type
Banach space
Cluster value
Fiber
Spectrum
spellingShingle Analytic functions of bounded type
Banach space
Cluster value
Fiber
Spectrum
Carando, Daniel German
Lassalle, Silvia Beatriz
Cluster values of holomorphic functions of bounded type
topic_facet Analytic functions of bounded type
Banach space
Cluster value
Fiber
Spectrum
description We study the cluster value theorem for Hb(X), the Fréchet algebra of holomorphic functions bounded on bounded sets of X. We also describe the (size of) fibers of the spectrum of Hb(X). Our results are rather complete whenever X has an unconditional shrinking basis and for X = ℓ1. As a byproduct, we obtain results on the spectrum of the algebra of all uniformly continuous holomorphic functions on the ball of ℓ1. © 2015 American Mathematical Society.
author Carando, Daniel German
Lassalle, Silvia Beatriz
author_facet Carando, Daniel German
Lassalle, Silvia Beatriz
author_sort Carando, Daniel German
title Cluster values of holomorphic functions of bounded type
title_short Cluster values of holomorphic functions of bounded type
title_full Cluster values of holomorphic functions of bounded type
title_fullStr Cluster values of holomorphic functions of bounded type
title_full_unstemmed Cluster values of holomorphic functions of bounded type
title_sort cluster values of holomorphic functions of bounded type
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029947_v368_n4_p2355_Aron
http://hdl.handle.net/20.500.12110/paper_00029947_v368_n4_p2355_Aron
work_keys_str_mv AT carandodanielgerman clustervaluesofholomorphicfunctionsofboundedtype
AT lassallesilviabeatriz clustervaluesofholomorphicfunctionsofboundedtype
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