Quasi-Multipliers on Banach Algebras Arising from Hypergroups

Ahmad Alinejad, Morteza Essmaili

Abstract

In this paper, we obtain a characterization for QM(L(X)), the quasi-multiplier algebra of L(X), where X is a foundation hypergroup . It is shown that QM(L(X)) can be identified by M(X) for this class of hypergroups. We also investigate quasi-multipliers on the second dual Banach algebra Lc(X)**. Indeed, we show that QM(Lc(X)**) is isomorphic with M(X). As an application, we prove that QM(Lc(X)**) = L(X) if and only if X is discrete.