Spectra of Algebras of Analytic Functions and Polynomials on Banach Spaces

Abstract

The paper contains a survey of basic facts about spectra of alge- bras of analytic functions of bounded type on Banach spaces and some new results in this area. In particular, we prove an analogue of Hilbert Nullstellensatz Theorem for polynomials on Banach spaces and investigate some derivations on algebras of analytic functions of bounded type which are associated with points of their spectra.