Quasi-multipliers on ℓ−algebras

In this paper we consider the notion of quasi-multipliers on an ℓ−algebra. We prove that, for a Banach ℓ−algebra A with an ultra approximate identity, the set ℓQM(A) of all order continuous ℓ−quasi-multipliers on A is a Banach f−algebra. Further, we establish the relationship between the space ℓQM(A) and the space ℓM(A) of all ℓ−multipliers on A. It is shown that, for certain Banach ℓ−algebra A, there exists a map φ : ℓM(A) → ℓQM(A) which is a positive, isometric and an algebraic lattice isomorphism.