Supersymmetric Polynomials on the Space of Absolutely Convergent Series

Abstract

We consider an algebra H b s u p of analytic functions on the Banach space of two-sided absolutely summing sequences which is generated by so-called supersymmetric polynomials. Our purpose is to investigate H b s u p and its spectrum with using methods of infinite dimensional complex analysis and the theory of Fréchet algebras. Some algebraic bases of H b s u p are described. Also, we show that the spectrum of the algebra of supersymmetric analytic functions of bounded type contains a metric ring M . We prove that M is a complete metric (nonlinear) space and investigate homomorphisms and additive operators on this ring. Some possible applications are discussed.