Cluster values of analytic functions on a Banach space

We investigate uniform algebras of bounded analytic functions on the unit ball of a complex Banach space. We prove several cluster value theorems, relating cluster sets of a function to its range on the fibers of the spectrum of the algebra. These lead to weak versions of the corona theorem for ℓ 2...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Carando, Daniel German, Lassalle, Silvia Beatriz
Publicado: 2012
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255831_v353_n2_p293_Aron
http://hdl.handle.net/20.500.12110/paper_00255831_v353_n2_p293_Aron
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00255831_v353_n2_p293_Aron
record_format dspace
spelling paper:paper_00255831_v353_n2_p293_Aron2023-06-08T14:53:19Z Cluster values of analytic functions on a Banach space Carando, Daniel German Lassalle, Silvia Beatriz We investigate uniform algebras of bounded analytic functions on the unit ball of a complex Banach space. We prove several cluster value theorems, relating cluster sets of a function to its range on the fibers of the spectrum of the algebra. These lead to weak versions of the corona theorem for ℓ 2 and for c 0. In the case of the open unit ball of c 0, we solve the corona problem whenever all but one of the functions comprising the corona data are uniformly approximable by polynomials in functions in c * 0. © 2011 Springer-Verlag. 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. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255831_v353_n2_p293_Aron http://hdl.handle.net/20.500.12110/paper_00255831_v353_n2_p293_Aron
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We investigate uniform algebras of bounded analytic functions on the unit ball of a complex Banach space. We prove several cluster value theorems, relating cluster sets of a function to its range on the fibers of the spectrum of the algebra. These lead to weak versions of the corona theorem for ℓ 2 and for c 0. In the case of the open unit ball of c 0, we solve the corona problem whenever all but one of the functions comprising the corona data are uniformly approximable by polynomials in functions in c * 0. © 2011 Springer-Verlag.
author Carando, Daniel German
Lassalle, Silvia Beatriz
spellingShingle Carando, Daniel German
Lassalle, Silvia Beatriz
Cluster values of analytic functions on a Banach space
author_facet Carando, Daniel German
Lassalle, Silvia Beatriz
author_sort Carando, Daniel German
title Cluster values of analytic functions on a Banach space
title_short Cluster values of analytic functions on a Banach space
title_full Cluster values of analytic functions on a Banach space
title_fullStr Cluster values of analytic functions on a Banach space
title_full_unstemmed Cluster values of analytic functions on a Banach space
title_sort cluster values of analytic functions on a banach space
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255831_v353_n2_p293_Aron
http://hdl.handle.net/20.500.12110/paper_00255831_v353_n2_p293_Aron
work_keys_str_mv AT carandodanielgerman clustervaluesofanalyticfunctionsonabanachspace
AT lassallesilviabeatriz clustervaluesofanalyticfunctionsonabanachspace
_version_ 1768541786607714304

Ejemplares similares