An example of a generalized completely continuous representation of a locally compact group
Volume 105 / 1993
Studia Mathematica 105 (1993), 189-205
DOI: 10.4064/sm-105-2-189-205
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".
