Zur Idealtheorie in Gruppenalgebren von [FIA] B − -Gruppen

In this paper we consider closedB-invariant ideals in the group algebraL ¹(G), whereG is a locally compact group with a relatively compact groupB of topological automorphisms, which contains the set of all inner automorphisms. We study conditions when closedB-invariant ideals are completely determined by their hull. Also questions concerning the existence of approximate units in these ideals will be answered. Above all, we shall study these properties with regard to the relations between ideals inL ¹(G),L ¹ (G/N) andL ¹(N), whereN is a closedB-invariant subgroup ofG.