The BSE property for vector-valued Frechet Lipschitz algebras

Abstract

Let $(X,d)$ be a metric space with at least two elements and $(A,p_l)$ be a commutative semisimple Frechet algebra over the scalar field of complex numbers. The correlation between the BSE-property of the Frechet algebra $(A,p_l)$ and $\Lip_{d}( X , A )$ is assessed. It is found and approved that if $\Lip_{d}( X , A )$ is a BSE-Frechet algebra, then so is $A$. The opposite correlation will hold if $(A,p_l)$ is unital.