Vol. 31, No. 3, 1969

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

Klaus R. Bichteler

Vol. 31 (1969), No. 3, 583–593

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
Received: 25 June 1968
Revised: 21 May 1969
Published: 1 December 1969
Klaus R. Bichteler