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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Processes disjoint from weak mixing

Authors: S. Glasner and B. Weiss
Journal: Trans. Amer. Math. Soc. 316 (1989), 689-703
MSC: Primary 28D05; Secondary 54H20
MathSciNet review: 946217
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Abstract: We show that the family $ {\mathcal{W}^ \bot }$ of ergodic measure preserving transformations which are disjoint from every weakly mixing m.p.t. properly contains the family $ \mathcal{D}$ of distal ergodic m.p.t. In the topological case we show that $ \mathcal{P}\mathcal{I}$, the family of proximally isometric flows is properly contained in the family $ \mathcal{M}({\mathcal{W}^ \bot })$ of multipliers for $ {\mathcal{W}^ \bot }$.

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

  • [F] H. Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation, Math. Systems Theory 1 (1967), 1-49. MR 0213508 (35:4369)
  • [G$ _{1}$] S. Glasner, Minimal skew products, Trans. Amer. Math. Soc. 260 (1980), 509-514. MR 574795 (82f:54069)
  • [G$ _{2}$] -, Quasi-factors in ergodic theory, Israel J. Math. 45 (1983), 198-208.
  • [G$ _{3}$] -, Proximal flows, Lecture Notes in Math., vol. 517, Springer-Verlag, 1976. MR 0474243 (57:13890)
  • [G-W] S. Glasner and B. Weiss, On the construction of minimal skew products, Israel J. Math. 34 (1979), 321-336. MR 570889 (82f:54068)
  • [G-H] W. H. Gottschalk and G. A. Hedlund, Topological dynamics, Amer. Math. Soc. Colloq. Publ., Vol. 36, Amer. Math. Soc., Providence, R.I., 1955. MR 0074810 (17:650e)
  • [M] D. McMahon, Multiple disjointness for weakly mixing regular minimal flows, Proc. Amer. Math. Soc. 98 (1986), 175-179. MR 848899 (87j:54062)
  • [N] M. G. Nerurkar, Ergodic continuous skew product actions of amenable groups, Pacific J. Math. 119 (1985), 343-363. MR 803124 (86m:28011)
  • [R] M. Ratner, Rigidity of horocycle flows, Ann. of Math. 115 (1982), 597-614. MR 657240 (84e:58062)
  • [Z] R. J. Zimmer, Ergodic actions with generalized discrete spectrum. Illinois J. Math. 20 (1975), 555-588. MR 0414832 (54:2924)

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Article copyright: © Copyright 1989 American Mathematical Society

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