The Bochner-Schoenberg-Eberlein module property for amalgamated duplication of Banach algebras

Authors : Mohammad Ali Abolfathi, Ali Ebadian, Ali Jabbari

Pages : 915-925

Doi:10.15672/hujms.1261110

View : 179 | Download : 255

Publication Date : 2024-08-27

Article Type : Research Paper

Abstract :The Bochner-Schoenberg-Eberlein module property on commutative Banach algebras is a property related to extensions of multipliers on Banach algebras to module morphisms from Banach algebras into Banach modules. In this paper, we answer the problem (1) raised in [J. Algebra Appl., 21(8) (2022), 2250155, DOI: 10.1142/S0219498822501559]. We show that the Banach $\\mathcal{A}\\rtimes\\mathfrak{A}$-module $X\\times Y$ ($X$ is a Banach $\\mathcal{A},\\mathfrak{A}$-module and $Y$ is a Banach $\\mathfrak{A}$-module) has a BSE-module property if and only if $X$ is a BSE Banach $\\mathcal{A},\\mathfrak{A}$-module and $Y$ is a BSE Banach $\\mathfrak{A}$-module.
Keywords : amalgamated Banach algebra, BSE Banach algebra, BSE module property, character, multiplier