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-*-algebraL 1(G) is annihilated by some nondegenerate continuous *-representation π ofL 1(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
LEPTIN, H.: On group algebras of nilpotent groups. Studia math.47, 37–49 (1973).
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WEIL, A.: L'intégration dans les groupes topologiques et ses applications, 2. Aufl. Paris: Hermann 1965.
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Heß, B. Über die Wiener-Eigenschaft bei projektiven Limites lokalkompakter Gruppen. Manuscripta Math 22, 209–212 (1977). https://doi.org/10.1007/BF01172662
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DOI: https://doi.org/10.1007/BF01172662