On the spectra of algebras of analytic functions

Abstract

In this paper we survey the most relevant recent developments on the research of the spectra of algebras of analytic functions. We concentrate mainly in three algebras, the Banach algebra H∞(B) of all bounded holomorphic functions on the unit ball B of a complex Banach space X, the Banach algebra of the ball Au(B), and the Fr´echet algebra Hb(X) of all entire functions bounded on bounded sets.