On characterizations of the image of Gelfand transform and BED property for vector valued ℓp−algebras

Abstract

Let X be a non-empty set, A be a commutative and semisimple Banach algebra and 1≤p<∞. In this paper, we first investigate the regularity and Tauberian property for the Banach algebra ℓp(X,A) and show that ℓp(X,A) is regular (resp. Tauberian) if and only if A is regular (resp. Tauberian). Then as the main result, we study the BED property for ℓp(X,A). Indeed, we establish that ℓp(X,A) is a BED algebra if and only if A is so. © 2022 Elsevier Inc.