The Bochner-Schoenberg-Eberlein Property for Fréchet C*-algebras and uniform Fréchet Algebras

The Bochner-Schoenberg-Eberlein property for commutative Frechet algebras

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. Furthermore, some of the main results in the class of Banach algebras, will be verified and generalized for the Frechet case.

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.

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。