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

TL;DR

This paper extends the Bochner-Schoenberg-Eberlein property from Banach algebras to a broader class of commutative Fréchet algebras, including Fréchet C*-algebras and uniform Fréchet algebras, establishing their BSE-algebra status.

Contribution

It introduces a new class of commutative Fréchet algebras satisfying the BSE-property and proves that certain important classes are included.

Findings

Fréchet C*-algebras are BSE-algebras

Uniform Fréchet algebras are BSE-algebras

Extension of BSE-property to Fréchet algebras

Abstract

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.