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

Studia Mathematica (1993)

- Volume: 105, Issue: 2, page 189-205
- ISSN: 0039-3223

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topPoguntke, Detlev. "An example of a generalized completely continuous representation of a locally compact group." Studia Mathematica 105.2 (1993): 189-205. <http://eudml.org/doc/215994>.

@article{Poguntke1993,

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”.},

author = {Poguntke, Detlev},

journal = {Studia Mathematica},

keywords = {generalized Heisenberg group; compactly generated, separable locally compact group; continuous irreducible unitary representation; group -algebra; algebra of compact operators; -group algebra; semidirect product},

language = {eng},

number = {2},

pages = {189-205},

title = {An example of a generalized completely continuous representation of a locally compact group},

url = {http://eudml.org/doc/215994},

volume = {105},

year = {1993},

}

TY - JOUR

AU - Poguntke, Detlev

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

JO - Studia Mathematica

PY - 1993

VL - 105

IS - 2

SP - 189

EP - 205

AB - 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”.

LA - eng

KW - generalized Heisenberg group; compactly generated, separable locally compact group; continuous irreducible unitary representation; group -algebra; algebra of compact operators; -group algebra; semidirect product

UR - http://eudml.org/doc/215994

ER -

## References

top- [1] J. Dixmier, Les C*-algèbres et leurs représentations, Gauthier-Villars, Paris 1969.
- [2] Ph. Green, The structure of imprimitivity algebras, J. Funct. Anal. 36 (1980), 88-104. Zbl0422.46048
- [3] A. Guichardet, Caractères des algèbres de Banach involutives, Ann. Inst. Fourier (Grenoble) 13 (1963), 1-81. Zbl0124.07003
- [4] H. Leptin, Verallgemeinerte ${L}^{1}$-Algebren und projektive Darstellungen lokal kompakter Gruppen, Invent. Math. 3 (1967), 257-281, 4 (1967), 68-86.
- [5] H. Leptin and D. Poguntke, Symmetry and nonsymmetry for locally compact groups, J. Funct. Anal. 33 (1979), 119-134. Zbl0414.43004
- [6] D. Poguntke, Unitary representations of Lie groups and operators of finite rank, Ann. of Math., to appear. Zbl0828.22013
- [7] H. Reiter, Classical Harmonic Analysis and Locally Compact Groups, Clarendon, Oxford 1968. Zbl0165.15601

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