Segal algebras on non-abelian groups

Let Sl(G) be a Segal algebra on a locally compact group.The central functions of S '(G) are dense in the center of L).S) has central approximate units iff G G [SIN].This is a generalization of a result of Reiter on the one hand and of Mosak on the other hand.The proofs depend on the structure theorems of [S/JV]-and [W]-groups.In the second part some new examples of Segal algebras are constructed.A locally compact group is discrete or Abelian iff every Segal algebra is rightinvariant.As opposed to the results, the proofs are not quite obvious.(AG [AH] denotes the Haar modules of G [FT]).THq is a linear operator of L) onto L/H) with IIWilier f^Lx(G), and THq{K(G)) = K(G/H).G operates weakly continuously on LX(G) via the isometric operators Ay,y E G, defined by