BSE PROPERTY OF FRÉCHET ALGEBRA

A class of commutative Banach algebras which satisfy a Bochner-Schoenberg-Eberlein-type inequality was introduced by Takahasi and Hatori. We generalize this property for the commutative Frechet algebra (A,pl)l is an element of N. Moreover, we verify and generalize some of the main results in the class of Banach algebras, for the Frechet case. We prove that all Frechet C*-algebras and also uniform Frechet algebras are BSE algebras. Also, we show that C infinity[0, 1] is not a Frechet BSE algebra.