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 of the -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”.
@article{bwmeta1.element.bwnjournal-article-smv105i2p189bwm,
author = {Detlev Poguntke},
title = {An example of a generalized completely continuous representation of a locally compact group},
journal = {Studia Mathematica},
volume = {104},
year = {1993},
pages = {189-205},
zbl = {0815.22002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv105i2p189bwm}
}
Poguntke, Detlev. An example of a generalized completely continuous representation of a locally compact group. Studia Mathematica, Tome 104 (1993) pp. 189-205. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv105i2p189bwm/
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