Spectra of Algebras of Entire Functions on Banach Spaces

Abstract

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