Weakly Completely Continuous Elements of the Banach Algebra LUC(G)*

In this paper, we study weakly compact left multipliers onthe banach algebra luc(g). we show that g is compact if and onlyif there exists a non-zero weakly compact left multipliers on luc(g).we also investigate the relation between positive left weakly completelycontinuous elements of the banach algebras luc(g) and l1(g). finally,we prove that g is finite if and only if there exists a non-zero multiplicativelinear functional ? on luc(g) such that ? is a left weaklycompletely continuous elements of luc(g).