Spectra of algebras of entire functions on Banach spaces

Abstract

We obtain an explicit description of the spectrum (set of closed maximal ideals) of H b ( X ) , H_b(X), algebra of analytic functions on a Banach space X X which are bounded on bounded subsets. We show that the spectrum of H b ( X ) 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 ⊂ X B\subset X are indicated.