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

TL;DR

This paper investigates conditions under which certain function spaces associated with a commutative Banach algebra and metric space are dual Banach algebras, contributing to the understanding of their duality properties.

Contribution

It establishes necessary and sufficient conditions for $ C_{BSE} ( riangle (A) ) $ and $ Lip_{eta} ( X , A ) $ to be dual Banach algebras, extending duality theory.

Findings

Characterization of dual Banach algebra conditions for $ C_{BSE} ( riangle (A) ) $

Conditions for $ Lip_{eta} ( X , A ) $ to be a dual Banach algebra

Extension of duality properties in Banach algebra function spaces

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.