An example of a generalized completely continuous representation of a locally compact group

Detlev Poguntke

ArticleOriginal scientific text

Title

An example of a generalized completely continuous representation of a locally compact group

Authors ¹

Affiliations

Universität Bielefeld, Fakultät Für Mathematik, Postfach 100131, W-4800 Bielefeld, Germany.

Abstract

There is constructed a compactly generated, separable, locally compact group G and a continuous irreducible unitary representation π of G such that the image π(C*(G)) of the group C*-algebra contains the algebra of compact operators, while the image

π (L^{1} (G))

of the

L^{1}

-group algebra does not containany nonzero compact operator. The group G is a semidirect product of a metabelian discrete group and a "generalized Heisenberg group".

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Title

An example of a generalized completely continuous representation of a locally compact group

Affiliations

Abstract

Bibliography