Weak Frobenius reciprocity and compactness conditions in topological groups

Rolf Wim Henrichs

Vol. 82 (1979), No. 2, 387–406

DOI: 10.2140/pjm.1979.82.387

Abstract

We study weak containment relations between unitary representations of a locally compact group G and closed subgroups H. We prove that certain weak Frobenius properties and compactness conditions are equivalent. Moreover, for amenable G having small invariant neighborhoods at e weak Frobenius reciprocity (FP) defined by Fell holds for the pair (G,H) if every element of H has relatively compact conjugacy class in G.

Mathematical Subject Classification 2000

Primary: 22D10

Secondary: 22D30

Milestones

Received: 1 December 1977

Revised: 16 October 1978

Published: 1 June 1979