JOININGS, INTERTWINING OPERATORS, FACTORS, AND MIXING PROPERTIES OF DYNAMICAL SYSTEMS

Abstract

This paper is mostly devoted to the following problem. If the Markov (stochastic) centralizer of a measure-preserving action is known, what can be said about the Markov centralizer of the action ? For a mixing flow with minimal Markov centralizer the author proves the triviality of the Markov centralizer of a Cartesian power of it, from which it follows that this flow possesses mixing of arbitrary multiplicity. For actions of the groups  the analogous assertion holds if their tensor product with themselves does not possess three pairwise independent factors. In particular, this is true for actions of  admitting a partial approximation and possessing mixing of multiplicity 2.