Quasi-multipliers on $\ell-$algebras

Document Type : Research Articles

Author

Department of mathematics, Payame Noor university, Tehran, Iran

Abstract

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.

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