On Banach algebras defined by multipliers

Abstract

In this paper, we investigate a Banach algebra AT, where A is a Banach algebra and T is a left (right) multiplier on A. We study some concepts on AT such as n-weak amenability, cyclic amenability, biflatness, biprojectivity and Arens regularity. For the group algebra L1(G) of an infinite compact group G, it is shown that there is a multiplier T such that L1(G)T has not a bounded approximate identity. For ?1(S), where S is a regular semigroup with a finite number of idempotents, we show that there is a multiplier T such that Arens regularity of ?1(S)T implies that S is compact.