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

• Autorzy: Detlev Poguntke
• Języki publikacji: EN

Abstrakty

EN

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".

Kategorie tematyczne

• 22D20: Representations of group algebras
• 22D10: Unitary representations of locally compact groups
• 22D25: C * -algebras and W * -algebras in relation to group representations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 105
• Numer: 2
• Strony: 189-205

Daty

wydano

1993

otrzymano

1992-12-18

Twórcy

autor

Detlev Poguntke

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

Bibliografia

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• [3] A. Guichardet, Caractères des algèbres de Banach involutives, Ann. Inst. Fourier (Grenoble) 13 (1963), 1-81.
• [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.
• [6] D. Poguntke, Unitary representations of Lie groups and operators of finite rank, Ann. of Math., to appear.
• [7] H. Reiter, Classical Harmonic Analysis and Locally Compact Groups, Clarendon, Oxford 1968.