REITER NETS FOR SEMIDIRECT PRODUCTS OF AMENABLE GROUPS AND SEMIGROUPS

In this paper we study Reiter nets for semidirect products of locally compact groups. A Reiter net is a net in L(1)(G)(1)(+) which satisfies Reiter's condition (P1). These are nets of means which converge to left invariance in norm uniformly on compact subsets of G. We provide two methods to combine Reiter nets for two groups to create a Reiter net for their semidirect product. We also present analogous results for combining Folner nets for locally compact groups and for Reiter nets for semidirect products of discrete semigroups.