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

2020/12/12 by Amiri, Mitra, Rejali, Ali
#46A04 (Primary) 46M40 #46K05 #47L40 (Secondary) #Commutative Algebra (math.AC) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2012.06887

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 Fréchet algebras which satisfy this property. We show that Fréchet C*-algebras and uniform Fréchet algebras are BSE-algebras.

Related

• The Bochner-Schoenberg-Eberlein property for commutative Frechet algebras
• Bochner-Schoenberg-Eberlein-type inequality of the direct sum, ideals and quotient of Frechet algebras
• The BSE property for vector-valued Frechet Lipschitz algebras
• BSE-Properties of Second Dual of Banach Algebras
• BSE-property of tensor product Banach algebras