Algebras of analytic functions on Banach spaces, generated by countable sets of polynomials and their properties

Abstract

In this work we investigate the properties of the topological algebras of entire functions, generated by countable sets ℙ={P1, . . . , Pn, . . .} of homogeneous polynomials on complex Banach spaces. In particular, we consider spectra Mbℙ of such algebras and the structure of the ranges of the spectra under the mapping τ : Mbℙ↦ℂ∞ such that τ(φ)=(φ(P1), φ(P2), . . .) for every φ∈Mbℙ. We also investigate conditions of isomorphism of such algebras. Some applications for algebras of symmetric analytic functions of bounded type are obtained.