  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.
