Displaying similar documents to “On the existence of unitary representations of commutative nuclear Lie groups”

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

Detlev Poguntke (1993)

Studia Mathematica

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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”.