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Weak Containment and Induced Representations of Groups

Published online by Cambridge University Press:  20 November 2018

J. M. G. Fell
J. M. G. Fell*
Affiliation:
University of Washington
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Let G be a locally compact group and G† its dual space, that is, the set of all unitary equivalence classes of irreducible unitary representations of G. An important tool for investigating the group algebra of G is the so-called hull-kernel topology of G†, which is discussed in (3) as a special case of the relation of weak containment. The question arises: Given a group G, how do we determine G† and its topology? For many groups G, Mackey's theory of induced representations permits us to catalogue all the elements of G†. One suspects that by suitably supplementing this theory it should be possible to obtain the topology of G† at the same time. It is the purpose of this paper to explore this possibility. Unfortunately, we are not able to complete the programme at present.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 14 , 1962 , pp. 237 - 268
Copyright
Copyright © Canadian Mathematical Society 1962

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