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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| Autores principales: | , , , , |
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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00255831_v353_n2_p293_Aron |
| Aporte de: |
| Sumario: | 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. |
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