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...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00255831_v353_n2_p293_Aron |
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todo:paper_00255831_v353_n2_p293_Aron2023-10-03T14:36:18Z Cluster values of analytic functions on a Banach space Aron, R.M. Carando, D. Gamelin, T.W. Lassalle, S. Maestre, M. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 |
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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. |
| format |
JOUR |
| author |
Aron, R.M. Carando, D. Gamelin, T.W. Lassalle, S. Maestre, M. |
| spellingShingle |
Aron, R.M. Carando, D. Gamelin, T.W. Lassalle, S. Maestre, M. Cluster values of analytic functions on a Banach space |
| author_facet |
Aron, R.M. Carando, D. Gamelin, T.W. Lassalle, S. Maestre, M. |
| author_sort |
Aron, R.M. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00255831_v353_n2_p293_Aron |
| work_keys_str_mv |
AT aronrm clustervaluesofanalyticfunctionsonabanachspace AT carandod clustervaluesofanalyticfunctionsonabanachspace AT gamelintw clustervaluesofanalyticfunctionsonabanachspace AT lassalles clustervaluesofanalyticfunctionsonabanachspace AT maestrem clustervaluesofanalyticfunctionsonabanachspace |
| _version_ |
1807324585137274880 |