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

2020/12/11 by Amiri, Mitra, Rejali, Ali
#46J05 (Primary) 46J20 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2012.06403

Abstract

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 ⊕ 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.

Related

• The Bochner-Schoenberg-Eberlein Property for Fréchet C*-algebras and uniform Fréchet Algebras
• The Bochner-Schoenberg-Eberlein property for commutative Frechet algebras
• The multiplier algebra and BSE-functions for certain product of Banach algebras
• The BSE property for vector-valued Frechet Lipschitz algebras
• Segal Frechet algebras