Structure space of tensor products of Frechet *-algebras

Abstract

In the case of a non-commutative m^*-convex algebra, the topological spectrum (Gel'fand space) of the commutative case is replaced by the structure space consisting of equivalent classes of continuous topologically irreducible representations. We prove that the structure space of a completed tensor product of two Frechet *-algebras is homeomorphic to the cartesian product of the structure spaces of the Frechet *-algebras involved.