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Weak disjointness of transformation groups

Author: Reuven Peleg
Journal: Proc. Amer. Math. Soc. 33 (1972), 165-170
MSC: Primary 54H15
MathSciNet review: 0298642
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Abstract: Two transformation groups (t.g.) are called weakly disjoint if their product is ergodic. We characterize this relation for a certain class of t.g. and then prove that for (X, T) and (Y, T) in a certain family of t.g. (X, T) and (Y, T) are disjoint iff they have no nontrivial common factor. Finally, we generalize some disjointness relations of [2] and [4].

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  • [1] H. Furstenberg, The structure of distal flows, Amer. J. Math. 85 (1963), 477-515. MR 28 #602. MR 0157368 (28:602)
  • [2] -, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Math. Systems Theory 1 (1967), 1-49. MR 35 #4369. MR 0213508 (35:4369)
  • [3] H. B. Keynes and J. B. Robertson, Eigenvalue theorems in topological transformation groups, Trans. Amer. Math. Soc. 139 (1969), 359-369. MR 38 #6029. MR 0237748 (38:6029)
  • [4] H. B. Keynes, The structure of weakly mixing transformation groups (preprint).
  • [5] R. Ellis, Lectures on topological dynamics, Benjamin, New York, 1969. MR 0267561 (42:2463)
  • [6] R. Ellis and H. Keynes, A Characterization of the equicontinuous structure relation (preprint). MR 0282357 (43:8069)
  • [7] L. Shapiro, Distal and proximal extensions of minimal flows, Math. Systems Theory 5 (1971), 76-88. MR 0301722 (46:877)

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Keywords: Transformation groups, disjointness, eigenvalues
Article copyright: © Copyright 1972 American Mathematical Society

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