Algebras of symmetric holomorphic functions on l_p

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Algebras of symmetric holomorphic functions on lp

We study the Banach algebra of uniformly continuous holomorphic symmetric functions on the unit ball of lp, investigating in particular the spectrum of such algebras. To do so, we 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.