The Bochner-Schoenberg-Eberlein Property for Fr\'echet C*-algebras and uniform Fr\'echet Algebras

Takahasi and Hatori introduced a class of commutative Banach algebras which satisfy a Bochner-Schoenberg-Eberlein-type inequality. Baised on their results we introduced a class of commutative Fr'echet algebras which satisfy this property. We show that Fr'echet C*-algebras and uniform Fr'echet algebras are BSE-algebras.