A characterization of compact groups
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- by George A. Elliott PDF
- Proc. Amer. Math. Soc. 29 (1971), 621 Request permission
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
- Larry Baggett, A separable group having a discrete dual space is compact, J. Functional Analysis 10 (1972), 131–148. MR 0346090, DOI 10.1016/0022-1236(72)90045-6
- Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173
- Shôichirô Sakai, On a characterization of type I $C^{\ast }$-algebras, Bull. Amer. Math. Soc. 72 (1966), 508–512. MR 192363, DOI 10.1090/S0002-9904-1966-11520-3
Additional Information
- © Copyright 1971 American Mathematical Society
- 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