The Bochner-Schoenberg-Eberlein property for commutative Frechet algebras

Bochner-Schoenberg-Eberlein-type inequality of the direct sum, ideals and quotient of Frechet algebras

Let A and B be two commutative semisimple Frechet algebras. We first give a characterization of the multiplier algebra of the direct sum of A and B. We then prove that A \oplus B is a BSE-algebra if and only if A and B are BSE-algebras. Furthermore, for a closed ideal I of A, we study multipliers of ideals and quotient algebras of A and show that I and A/I are BSE-algebras, under certain conditions.

The Bochner-Schoenberg-Eberlein Property for Fréchet C*-algebras and uniform Fréchet 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 Fréchet algebras which satisfy this property. We show that Fréchet C*-algebras and uniform Fréchet algebras are BSE-algebras.

Dirichlet级数的加权Banach代数的BSE性质

The BSE Property for Weighted Banach Algebras of Dirichlet Series

本文研究Dirichlet级数加权Banach代数的BSE性质，通过Bohr对应和弱-*逼近框架，证明对任意权重该代数为BSE-代数，且内在BSE范数与加权范数等距。