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

Kallman, Robert R.

doi:10.1090/S0002-9939-1973-0316630-5

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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A theorem on the restriction of type I representations of a group to certain of its subgroups
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by Robert R. Kallman PDF

Proc. Amer. Math. Soc. 40 (1973), 291-296 Request permission

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 $\pi |H$ is Type I.

References

Jacques Dixmier, Les algèbres d’opérateurs dans l’espace hilbertien (Algèbres de von Neumann), Cahiers Scientifiques, Fasc. XXV, Gauthier-Villars, Paris, 1957 (French). MR 0094722
Robert R. Kallman, A generalization of free action, Duke Math. J. 36 (1969), 781–789. MR 256181
Robert R. Kallman, Certain topological groups are type I, Bull. Amer. Math. Soc. 76 (1970), 404–406. MR 255725, DOI 10.1090/S0002-9904-1970-12491-0