On the structure of Gelfand transform and BED property for abstract Segal algebras

Abstract

Let (Formula presented) be a commutative and semisimple Banach algebra and (B, ∥ · ∥B) be an abstract Segal algebra with respect to A. In this paper, we first show that A is Tauberian if and only if B is Tauberian. Then we prove that (Formula presented) if and only if (Formula presented). Afterwards, we conclude that whenever BSE BSE A is a BED algebra, then B is a BED algebra if and only if (Formula presented). © 2025, University of Nis. All rights reserved.