BSE-property of tensor product Banach algebras

TL;DR

This paper investigates the BSE and BED properties of tensor product Banach algebras, especially focusing on vector-valued group and C*-algebras, providing new characterizations of their structure.

Contribution

It offers new insights into the BSE and BED properties of tensor product Banach algebras, including vector-valued group and C*-algebras, with specific characterizations.

Findings

Characterization of BSE and BED properties for tensor Banach algebras

Analysis of vector-valued group algebra $L_{1}(G, A)$

Analysis of $C^{*}$-algebra $C_{0}(X, A)$

Abstract

Let $A$ and $B$ be commutative semisimple Banach algebras. In this paper, the $BSE$ and $BED$- property of tensor Banach algebra $A{\otimes}_{\gamma} B$ with respect to the Banach algebras $A$ and $B$ are assesed. In particular, $BSE$ and $BED$- structure of vector-valued group algebra $L_{1}(G, A)$ and $C^{*}$- algebra $C_{0}(X, A)$ characterized.