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Two facts concerning the transformations which satisfy the weak Pinsker property

Published online by Cambridge University Press:  01 April 2008

J.-P. THOUVENOT
J.-P. THOUVENOT*
Affiliation:
Laboratoire de Probabilites et Modeles Aleatoires, UMR 7599, Universites Paris 6 et Paris 7, Boite Courrier 188, 4, Place Jussieu, 75252 Paris Cedex 05, France (email: [email protected])
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Abstract

We show that every ergodic, finite entropy transformation which satisfies the weak Pinsker property possesses a finite generator whose two-sided tail field is exactly the Pinsker algebra. This is proved by exhibiting a generator endowed with a block structure quite analogous to the one appearing in the construction of the Ornstein–Shields examples of non Bernoulli K-automorphisms. We also show that, given two transformations T1 and T2 in the previous class (i.e. satisfying the weak Pinsker property), and a Bernoulli shift B, if T1×B is isomorphic to T2×B, then T1 is isomorphic to T2. That is, one can ‘factor out’ Bernoulli shifts.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 2: William Parry Memorial Volume , April 2008 , pp. 689 - 695
Copyright
Copyright © Cambridge University Press 2008

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References

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