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A characterization of compact groups


Author: George A. Elliott
Journal: Proc. Amer. Math. Soc. 29 (1971), 621
MSC: Primary 22.20
DOI: https://doi.org/10.1090/S0002-9939-1971-0276408-6
MathSciNet review: 0276408
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Abstract: A locally compact group is compact if and only if it is of type I and has discrete spectrum (equivalently: its $ {C^\ast}$-algebra is dual).


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

  • [1] L. Baggett, A separable group having a discrete dual space is compact (preprint). MR 0346090 (49:10816)
  • [2] J. Dixmier, Les $ {C^\ast}$-algèbres et leurs représentations, Cahiers Scientifiques, fasc. 29, Gauthier-Villars, Paris, 1964. MR 30 #1404. MR 0171173 (30:1404)
  • [3] S. Sakai, On a characterization of type I $ {C^\ast}$-algebras, Bull. Amer. Math. Soc. 72 (1966), 508-512. MR 33 #588. MR 0192363 (33:588)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0276408-6
Keywords: Group $ {C^\ast}$-algebra, dual $ {C^\ast}$-algebra, compact group, Lie group
Article copyright: © Copyright 1971 American Mathematical Society

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