Quasi-multipliers on \ell-algebras

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

کلیدواژه ها:

Multiplier ، Quasi-multiplier‎ ، ‎‎ ‎\ell-space‎ ، ‎Banach \ell-algebra