V. V. Ryzhikov, J.-P. Thouvenot, “On the Centralizer of an Infinite Mixing Rank-One Transformation”, Funktsional. Anal. i Prilozhen., 2015, Volume 49, Issue 3,Pages <nobr>88

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Brief communications

On the Centralizer of an Infinite Mixing Rank-One Transformation

V. V. Ryzhikov^a, J.-P. Thouvenot^b

^a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Université Pierre & Marie Curie, Paris VI

Abstract: A property of minimal self-joinings for mixing rank-one transformations preserving the measure of an infinite Lebesgue space is established. Its main consequence is the triviality of the centralizer of such transformations.

Keywords: mixing, rank-one transformation, sigma-finite measure, minimal self-joinings.

UDC: 517.9

Received: 17.02.2014

DOI: 10.4213/faa3207