Approximate Units in Ideals of Group Algebras

Abstract

Several properties of locally compact groups can be characterized by the existence of certain approximate units in 3 ideals of the group algebra. We combine methods and results from [8], [7], [5]. Let G be a locally compact group, M(G) the Banach algebra of all bounded complex measures, LX(G) the ideal consisting of all absolutecontinuous measures with respect to left Haar-measure,