$C_{BSE}(\Delta (A))$ as a dual Banach algebra

Abstract

Let $(X,d)$ be a metric space and $A$ be a commutative Banach algebra such that $\Delta (A)$ be nonempty. In this paper, we provide necessary and sufficient conditions, under which $C_{BSE}(\Delta (A))$ is a Dual Banach algebra. Moreover, we provide some conditions for that $Li{p}_{\alpha }(X,A)$ is a Dual Banach algebra.