We study compact and weakly compact multipliers on L ( S ) , L ( S ) * * , and L U C ( S ) * , where the latter is the dual of L U C ( S ) . We show that a left cancellative semigroup S is left amenable if and only if there is a nonzero compact (or weakly compact) multiplier on L ( S ) * * . We also prove that S is left amenable if and only if there is a nonzero compact (or weakly compact) multiplier on L U C ( S ) * .