Spectra of algebras of entire functions on Banach spaces

Zagorodnyuk, Andriy

doi:10.1090/S0002-9939-06-08260-8

Spectra of algebras of entire functions on Banach spaces
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Proc. Amer. Math. Soc. 134 (2006), 2559-2569 Request permission

Abstract:

We obtain an explicit description of the spectrum (set of closed maximal ideals) of $H_b(X),$ algebra of analytic functions on a Banach space $X$ which are bounded on bounded subsets. We show that the spectrum of $H_b(X)$ admits a natural linear structure. Some applications to the algebra of uniformly continuous and bounded analytic functions on the unit ball $B\subset X$ are indicated.

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