Characterizing mildly mixing actions by orbit equivalence of products.
Hawkins, Jane, Silva Cesar, E. (1998)
The New York Journal of Mathematics [electronic only]
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Hawkins, Jane, Silva Cesar, E. (1998)
The New York Journal of Mathematics [electronic only]
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D. de Schreye (1985)
Mathematica Scandinavica
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Su Gao, Vladimir Pestov (2003)
Fundamenta Mathematicae
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We show that every abelian Polish group is the topological factor group of a closed subgroup of the full unitary group of a separable Hilbert space with the strong operator topology. It follows that all orbit equivalence relations induced by abelian Polish group actions are Borel reducible to some orbit equivalence relations induced by actions of the unitary group.
Alexandre Danilenko, Toshihiro Hamachi (2000)
Colloquium Mathematicae
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The orbit equivalence of type ergodic equivalence relations is considered. We show that it is equivalent to the outer conjugacy problem for the natural trace-scaling action of a countable dense ℝ-subgroup by automorphisms of the Radon-Nikodym skew product extensions of these relations. A similar result holds for the weak equivalence of arbitrary type cocycles with values in Abelian groups.
Furman, Alex (1999)
Annals of Mathematics. Second Series
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Raja, C.Robinson Edward (2009)
The New York Journal of Mathematics [electronic only]
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Alexandre I. Danilenko, Cesar E. Silva (2007)
Annales de l'I.H.P. Probabilités et statistiques
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D. de Schreye (1983)
Mathematica Scandinavica
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Robert J. Zimmer (1978)
Annales scientifiques de l'École Normale Supérieure
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Charles Pugh, Michael Shub (1971)
Compositio Mathematica
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Valentin Golodets, Sergey Sinel'shchikov (2000)
Colloquium Mathematicae
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The existence of non-Bernoullian actions with completely positive entropy is proved for a class of countable amenable groups which includes, in particular, a class of Abelian groups and groups with non-trivial finite subgroups. For this purpose, we apply a reverse version of the Rudolph-Weiss theorem.
Greg Hjorth (2009)
Fundamenta Mathematicae
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A countable group Γ has the Haagerup approximation property if and only if the mixing actions are dense in the space of all actions of Γ.