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manuscripta mathematica

, Volume 22, Issue 3, pp 209–212 | Cite as

Über die Wiener-Eigenschaft bei projektiven Limites lokalkompakter Gruppen

  • Bernhard Heß
Article

Abstract

Leptin posed in [1] the problem to determine the class [W] of locally compact groups G characterized by the following property: Every proper closed two-sided idealJ in the Banach-*-algebraL1(G) is annihilated by some nondegenerate continuous *-representation π ofL1(G) in a Hilbert space. Our main result: A locally compact group G, which is representable as a projective limit of a system of factor groups G/k, k compact normal subgroups, lies in [W] if and only if all the G/k are in [W].

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Literatur

  1. [1]
    LEPTIN, H.: On group algebras of nilpotent groups. Studia math.47, 37–49 (1973).Google Scholar
  2. [2]
    —: Ideal theory in group algebras of locally compact groups. Inventiones math.31, 259–278 (1976).Google Scholar
  3. [3]
    MONTGOMERY, D., u. L. ZIPPIN: Topological transformation groups, 4. Aufl. New YorK: Interscience 1966.Google Scholar
  4. [4]
    WEIL, A.: L'intégration dans les groupes topologiques et ses applications, 2. Aufl. Paris: Hermann 1965.Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Bernhard Heß
    • 1
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeld 1

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