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- W2188128843 abstract "Using Gaussian cocycles over a mixing Gaussian au- tomorphism T, we construct two mixing extensions of T which are Markov quasi-equivalent and are not weakly isomorphic. Assume that (X;B; ) is a probability standard Borel space and let T be its automorphism. Then T induces a unitary Koopman operator UT acting on L 2 (X;B; ) by the formula UTf = f T. Note that UT is an example of a Markov operator (i.e. of a continuous linear operator between L 2 -spaces, doubly stochastic and preserving the cone of non- negative functions. In (12), Vershik introduced the concept of Markov quasi-equivalence (MQ-equiv.) between automorphisms, namely, if Ti is an automor- phism of (Xi;Bi; i), i = 1; 2, then T1 and T2 are said to be MQ-equiv. if there are Markov operators : L 2 (X1;B1; 1)! L 2 (X2;B2; 2); : L 2 (X2;B2; 2)! L 2 (X1;B1; 1)" @default.
- W2188128843 created "2016-06-24" @default.
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- W2188128843 date "2013-12-09" @default.
- W2188128843 modified "2023-09-26" @default.
- W2188128843 title "Mixing Automorphisms which are Markov Quasi-Equivalent but not Weakly Isomorphic" @default.
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- W2188128843 doi "https://doi.org/10.1515/9783110298208.129" @default.
- W2188128843 hasPublicationYear "2013" @default.
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