Noncommutative topological dynamics. I
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- by Daniel Avitzour
- Trans. Amer. Math. Soc. 282 (1984), 109-119
- DOI: https://doi.org/10.1090/S0002-9947-1984-99926-0
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Part II: Trans. Amer. Math. Soc. (1) (1984), 121-135
Abstract:
Ergodicity and minimality are defined for $C^{\ast }$-flows $(G,A)$ where $G$ is a group acting on a $C^{\ast }$-algebra $A$ by *-automorphisms. Elementary properties are proved and several examples are given. In particular, an example shows that there are arbitrarily large $C^{\ast }$-algebras admitting a minimal action of the integers.References
- E. M. Alfsen and F. W. Schultz, Noncommutative spectral theory for affine function spaces on convex sets, Mem. Amer. Math. Soc. No. 172 (1976).
- Daniel Avitzour, Free products of $C^{\ast }$-algebras, Trans. Amer. Math. Soc. 271 (1982), no. 2, 423–435. MR 654842, DOI 10.1090/S0002-9947-1982-0654842-1 —, Noncommutative topological dynamics. II, Trans. Amer. Math. Soc. 282(1984), 121-135.
- Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173
- Edward G. Effros, Order ideals in a $C^{\ast }$-algebra and its dual, Duke Math. J. 30 (1963), 391–411. MR 151864
- H. Furstenberg, The structure of distal flows, Amer. J. Math. 85 (1963), 477–515. MR 157368, DOI 10.2307/2373137
- Harry Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Math. Systems Theory 1 (1967), 1–49. MR 213508, DOI 10.1007/BF01692494
- Alain Guichardet, Systèmes dynamiques non commutatifs, Astérisque, Nos. 13-14, Société Mathématique de France, Paris, 1974 (French). With an English summary; Séminaire rédigé par A. Guichardet d’après des exposés faits au Séminaire Dang Ngoc—Guichardet 1972-1973 par C. Cahmbon, F. Combes, N. Dang Ngoc, M. Enock, A. Guichardet, F. Ledrappier, J. C. Marcuard, O. Maréchal, M. Samuélidès, J. L. Sauvageot, J. M. Schwartz, J. P. Thouvenot. MR 0352997
- Harvey B. Keynes and James B. Robertson, On ergodicity and mixing in topological transformation groups, Duke Math. J. 35 (1968), 809–819. MR 234441
- Harvey B. Keynes and James B. Robertson, Eigenvalue theorems in topological transformation groups, Trans. Amer. Math. Soc. 139 (1969), 359–369. MR 237748, DOI 10.1090/S0002-9947-1969-0237748-5
- Diane Laison and Gary Laison, Topological dynamics on $C^*$-algebras, Trans. Amer. Math. Soc. 204 (1975), 197–205. MR 358365, DOI 10.1090/S0002-9947-1975-0358365-5
- Gert K. Pedersen, $C^{\ast }$-algebras and their automorphism groups, London Mathematical Society Monographs, vol. 14, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1979. MR 548006
- William A. Veech, Finite group extensions of irrational rotations, Israel J. Math. 21 (1975), no. 2-3, 240–259. MR 396913, DOI 10.1007/BF02760801
Bibliographic Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 282 (1984), 109-119
- MSC: Primary 46L55; Secondary 54H20
- DOI: https://doi.org/10.1090/S0002-9947-1984-99926-0
- MathSciNet review: 728705