ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 43A20 Medghalchi, A. R., and S. M. S. Modarres, Inst. Math., Teacher Training University, Tehran, Iran Amenability of the second dual of hypergroup algebras The amenability of the Banach algebra L^{1}(G), of the measure algebra M(G) and of their second duals, for a locally compact group G, have been considered by a number of authors. During these investigations it has been shown that L^{1}(G)^{∗∗} is amenable if and only if G is finite. If LUC(G^{∗}), the dual of the space of left uniformly continuous functions on G, is amenable, then G is compact and M(G) is amenable. Finally, if M(G)^{∗∗} is amenable, then G is finite. The aim of this paper is to generalize all of the above results to locally compact hypergroups.