Noncommutative topological dynamics. II
HTML articles powered by AMS MathViewer
- by Daniel Avitzour PDF
- Trans. Amer. Math. Soc. 282 (1984), 121-135 Request permission
Abstract:
This part deals with almost periodic and weakly mixing ${C^ \ast }$-flows, and with disjointness and weak disjointness of ${C^ \ast }$-flows (flows on ${C^ \ast }$-algebras). The main result is a generalization to ${C^ \ast }$-flows of Keynes and Robertson’s characterization of minimal weakly mixing flows. Examples are discussed exhibiting anomalous behaviour of disjointness in the ${C^ \ast }$-flow case.References
- Daniel Avitzour, Noncommutative topological dynamics. I, II, Trans. Amer. Math. Soc. 282 (1984), no. 1, 109–119, 121–135. MR 728705, DOI 10.1090/S0002-9947-1984-0728705-9
- 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
- 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
- William L. Green, Topological dynamics and $C^{\ast }$-algebras, Trans. Amer. Math. Soc. 210 (1975), 107–121. MR 383091, DOI 10.1090/S0002-9947-1975-0383091-6
- 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 D. Oleson, G. K. Pedersen and M. Takesaki, Ergodic actions of compact Abelian groups, Copenhagen Preprint Series No. 19, 1979.
- 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
- Reuven Peleg, Weak disjointness of transformation groups, Proc. Amer. Math. Soc. 33 (1972), 165–170. MR 298642, DOI 10.1090/S0002-9939-1972-0298642-2
- Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173
- Masamichi Takesaki, Theory of operator algebras. I, Springer-Verlag, New York-Heidelberg, 1979. MR 548728
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 282 (1984), 121-135
- MSC: Primary 46L55; Secondary 54H20
- DOI: https://doi.org/10.1090/S0002-9947-1984-0728705-9
- MathSciNet review: 728705