$C_{BSE}(\Delta(A))$ 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 $ Lip_{\alpha} ( X , A ) $ is a Dual Banach algebra.