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On isomorphity of measure-preserving ℤ2-actions that have isomorphic Cartesian powers

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Abstract

Assume that Δ and Π are representations of the group ℤ2 by operators on the space L 2(X, μ) that are induced by measure-preserving automorphisms, and for some d, the representations Δ⨂d and Π⨂d are conjugate to each other, Δ(ℤ2 \(0, 0)) consists of weakly mixing operators, and there is a weak limit (over some subsequence in ℤ2 of operators from Δ(ℤ2)) which is equal to a nontrivial, convex linear combination of elements of Δ(ℤ2) and of the projection onto constant functions. We prove that in this case, Δ and Π are also conjugate to each other.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    A. E. Troitskaya

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  1. A. E. Troitskaya
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Correspondence to A. E. Troitskaya.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 8, pp. 193–212, 2007.

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Troitskaya, A.E. On isomorphity of measure-preserving ℤ2-actions that have isomorphic Cartesian powers. J Math Sci 159, 879–893 (2009). https://doi.org/10.1007/s10958-009-9478-z

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