# Algebras of symmetric holomorphic functions on l_p

**Source**: https://www.maths.tcd.ie/report_series/abstracts/tcdm0013.html
**Parent**: https://www.maths.tcd.ie/research/papers/

**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.