ALGEBRAS OF SYMMETRIC HOLOMORPHIC FUNCTIONS ON ${\cal L}_p$

Abstract

The authors study the algebra of uniformly continuous holomorphic symmetric functions on the ball of lp, investigating in particular the spectrum of such algebras. To do so, they examine the algebra of symmetric polynomials on lp-spaces, as well as finitely generated symmetric algebras of holomorphic functions. Such symmetric polynomials determine the points in lp up to a permutation.