Locally Compact Groups Satisfying Chu Duality Respect Compactness
by
F. Javier Trigos-Arrieta
California State University, Bakersfield
Coauthors: Dieter Remus

For a locally compact (LC) group G , denote by G+ its underlying group equipped with the topology inherited from its Bohr compactification. G is maximally almost periodic (MAP) if and only if G+ is Hausdorff. A MAP group G respects compactness if G and G+ have the same compact sets. In 1962 I. Glicksberg proved that LC Abelian groups respect compactness. More recently we have extended Glicksberg's result to the class [MOORE], which is defined as the class of LC groups such that all their continuous irreducible unitary representations are finite-dimensional. This also follows from a result of R. Hughes in 1973. We asked in turn if there are any LC groups outside the class [MOORE], still respecting compactness. In this presentation we answer this question positively by showing that groups satisfying Chu duality respect compactness.

Date received: April 12, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaf-86.