Locally compact topologies on a group and the corresponding continuous irreducible representations

Klaus R. Bichteler

Vol. 31 (1969), No. 3, 583–593

DOI: 10.2140/pjm.1969.31.583

Abstract

It is shown that two different topologies on a group G both of which make it into a locally compact group, usually give rise to different continuous irreducible unitary representations. To be more precise: If the continuous irreducible unitary representations of G coincide for the two topologies, then these topologies are the same in the following cases: The topologies are comparable; There exists a normal subgroup of G, open and σ-compact in one of the topologies.

Mathematical Subject Classification

Primary: 22.60

Milestones

Received: 25 June 1968

Revised: 21 May 1969

Published: 1 December 1969