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