The BSE property for some vector-valued Banach function algebras

Abstract

In this paper, X is a locally compact Hausdorff space and A is a Banach algebra. First, we study some basic features of C0(X, A) related to BSE concept, which are gotten from A. In particular, we prove that if C0(X, A) has the BSE property then A has so. We also establish the converse of this result, whenever X is discrete and A has the BSE-norm property. Furthermore, we prove the same result for the BSE property of type I. Finally, we prove that C0 (X, A) has the BSE-norm property if and only if A has so. © Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences 2024.