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A theorem on the restriction of type I representations of a group to certain of its subgroups


Author: Robert R. Kallman
Journal: Proc. Amer. Math. Soc. 40 (1973), 291-296
MSC: Primary 22D10; Secondary 46L10
DOI: https://doi.org/10.1090/S0002-9939-1973-0316630-5
MathSciNet review: 0316630
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Abstract: Theorem. Let $ G$ be a separable locally compact group and $ H$ a closed subgroup such that $ G/H$ is finite. Let $ \pi $ be a Type I representation of $ G$. Then $ \pi \vert H$ is Type I.


References [Enhancements On Off] (What's this?)

  • [1] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, Gauthier-Villars, Paris, 1957. MR 20 #1234. MR 0094722 (20:1234)
  • [2] Robert R. Kallman, A generalization of free action, Duke Math. J. 36 (1969), 781-789. MR 41 #838. MR 0256181 (41:838)
  • [3] -, Certain topological groups are type I, Bull. Amer. Math. Soc. 76 (1970), 404-406. MR 41 #385. MR 0255725 (41:385)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0316630-5
Keywords: Operator theory, von Neumann algebras, group representations
Article copyright: © Copyright 1973 American Mathematical Society

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