Uniqueness of F-Algebra Topology for Commutative Semisimple Algebras

Abstract

Let A be a complex commutative semisimple complete LMC algebra with respect to a topology $$\tau _{1}$$ and a complete metrizable topological algebra with respect to a topology $$\tau _{2}$$ . It is proved that every $$\tau _{1}$$ -bounded set is a $$\tau _{2}$$ -bounded set. This generalizes a result of R. L. Carpenter on uniqueness of Frechet algebra topology for complex commutative semisimple algebras.