Arens regularity and discrete groups

Brian E. Forrest

Vol. 151 (1991), No. 2, 217–227

DOI: 10.2140/pjm.1991.151.217

Abstract

Let G be a locally compact group. Let A_p(G) be the Herz algebra of G associated with 1 < p < ∞. We show that if A_p(G) is Arens regular, then G is discrete. We also exhibit a number of sufficient conditions for such a group to be finite.

Mathematical Subject Classification 2000

Primary: 43A15

Secondary: 43A30, 46H05

Milestones

Received: 12 July 1990

Revised: 2 November 1990

Published: 1 December 1991