Reiter nets for semidirect products of amenable groups and semigroups

Willson, Benjamin

doi:10.1090/S0002-9939-09-09957-2

Reiter nets for semidirect products of amenable groups and semigroups
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Proc. Amer. Math. Soc. 137 (2009), 3823-3832 Request permission

Abstract:

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 Følner nets for locally compact groups and for Reiter nets for semidirect products of discrete semigroups.

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