The BSE Property for Vector-Valued Frechet Lipschitz Algebras

Abstract

Let (X, d) be a metric space with at least two elements and (A, pl) be a commutative semisimple Frechet algebra over the scalar field C. The correlation between the BSE-property of the Frechet algebra (A, pl) and Lipd(X,A) is assessed. It is found and approved that if Lipd(X,A) is a BSEFrechet algebra, then so is A. The opposite correlation will hold if (A, pl) is unital.