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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Detalles Bibliográficos
Autores principales:	Aron, R.M., Carando, D., Lassalle, S., Maestre, M.
Formato:	JOUR
Materias:	Analytic functions of bounded type Banach space Cluster value Fiber Spectrum
Acceso en línea:	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	todo:paper_00029947_v368_n4_p2355_Aron
record_format	dspace
spelling	todo:paper_00029947_v368_n4_p2355_Aron2023-10-03T13:55:23Z Cluster values of holomorphic functions of bounded type Aron, R.M. Carando, D. Lassalle, S. Maestre, M. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Aron, R.M. Carando, D. Lassalle, S. Maestre, M. 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.
format	JOUR
author	Aron, R.M. Carando, D. Lassalle, S. Maestre, M.
author_facet	Aron, R.M. Carando, D. Lassalle, S. Maestre, M.
author_sort	Aron, R.M.
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
url	http://hdl.handle.net/20.500.12110/paper_00029947_v368_n4_p2355_Aron
work_keys_str_mv	AT aronrm clustervaluesofholomorphicfunctionsofboundedtype AT carandod clustervaluesofholomorphicfunctionsofboundedtype AT lassalles clustervaluesofholomorphicfunctionsofboundedtype AT maestrem clustervaluesofholomorphicfunctionsofboundedtype
_version_	1807322087927316480

Cluster values of holomorphic functions of bounded type

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