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Funktsional. Anal. i Prilozhen., 2015, Volume 49, Issue 3, Pages 88–91 (Mi faa3207)  

This article is cited in 5 scientific papers (total in 5 papers)

Brief communications

On the Centralizer of an Infinite Mixing Rank-One Transformation

V. V. Ryzhikova, J.-P. Thouvenotb

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

DOI: https://doi.org/10.4213/faa3207

Full text: PDF file (123 kB)
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English version:
Functional Analysis and Its Applications, 2015, 49:3, 230–233

Bibliographic databases:

UDC: 517.9
Received: 17.02.2014

Citation: V. V. Ryzhikov, J.-P. Thouvenot, “On the Centralizer of an Infinite Mixing Rank-One Transformation”, Funktsional. Anal. i Prilozhen., 49:3 (2015), 88–91; Funct. Anal. Appl., 49:3 (2015), 230–233

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. V. Klimov, V. V. Ryzhikov, “Minimal Self-Joinings of Infinite Mixing Actions of Rank 1”, Math. Notes, 102:6 (2017), 787–791  mathnet  crossref  crossref  isi  elib
    2. J. Gaebler, A. Kastner, C. E. Silva, X. Xu, Z. Zhou, “Partially bounded transformations have trivial centralizers”, Proc. Amer. Math. Soc., 146:12 (2018), 5113–5127  crossref  mathscinet  zmath  isi
    3. C. Bonanno, P. Giulietti, M. Lenci, “Infinite mixing for one-dimensional maps with an indifferent fixed point”, Nonlinearity, 31:11 (2018), 5180–5213  crossref  zmath  isi  scopus
    4. V. V. Ryzhikov, “Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows”, Math. Notes, 104:6 (2018), 900–904  mathnet  crossref  crossref  isi  elib
    5. V. V. Ryzhikov, “Weak Closure of Infinite Actions of Rank 1, Joinings, and Spectrum”, Math. Notes, 106:6 (2019), 957–965  mathnet  crossref  crossref  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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