On the structure of quasi-topology and BED property for direct sum of Banach algebras

Abstract

Let (A, ‖ · ‖ A) and (B, ‖ · ‖ B) be commutative and semisimple Banach algebras. In this paper, we verify the BED property for the direct sum of A and B, denoted by A⊕ B. In particular, we show that A⊕ B is a BED algebra if and only if A and B are so. © 2022, Akadémiai Kiadó, Budapest, Hungary.