SOME ALGEBRAS OF SYMMETRIC ANALYTIC FUNCTIONS AND THEIR SPECTRA

Abstract

In the spectrum of the algebra of symmetric analytic functions of bounded type on p, 1 p < +∞, and along the same lines as the general non-symmetric case, we define and study a convolution operation and give a formula for the ‘radius’ function. It is also proved that the algebra of analytic functions of bounded type on 1 is isometrically isomorphic to an algebra of symmetric analytic functions on a polydisc of 1. We also consider the existence of algebraic projections between algebras of symmetric polynomials and the corresponding subspace of subsymmetric polynomials.