COMPACT LEFT MULTIPLIERS ON BANACH ALGEBRAS RELATED TO LOCALLY COMPACT GROUPS

Abstract

Abstract We deal with the dual Banach algebras $L_0^\infty (G)^*$ for a locally compact group G . We investigate compact left multipliers on $L_0^\infty (G)^*$ , and prove that the existence of a compact left multiplier on $L_0^\infty (G)^*$ is equivalent to compactness of G . We also describe some classes of left completely continuous elements in $L_0^\infty (G)^*$ .