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Funktsional'nyi Analiz i ego Prilozheniya, 2015, Volume 49, Issue 3, Pages 88–91
DOI: https://doi.org/10.4213/faa3207 (Mi faa3207) 		 
This article is cited in 9 scientific papers (total in 9 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
Full-text PDF (123 kB) Citations (9)
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DOI: https://doi.org/10.4213/faa3207
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.
Received: 17.02.2014
English version:
Functional Analysis and Its Applications, 2015, Volume 49, Issue 3, Pages 230–233
DOI: https://doi.org/10.1007/s10688-015-0111-2
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
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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  • https://www.mathnet.ru/eng/faa3207
  • https://doi.org/10.4213/faa3207
  • https://www.mathnet.ru/eng/faa/v49/i3/p88
    • This publication is cited in the following 9 articles:
    1. V. V. Ryzhikov, “Zhestkie puassonovskie nadstroiki bez kornei”, Matem. zametki, 117:1 (2025), 146–150  mathnet  crossref
    2. Alexandre I. Danilenko, Cesar E. Silva, Encyclopedia of Complexity and Systems Science Series, Ergodic Theory, 2023, 233  crossref
    3. Alexandre I. Danilenko, Cesar E. Silva, Encyclopedia of Complexity and Systems Science, 2022, 1  crossref
    4. V. V. Ryzhikov, “Measure-preserving rank one transformations”, Trans. Moscow Math. Soc., 81:2 (2020), 229–259  mathnet  crossref  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  mathscinet  isi  elib
    6. 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  scopus
    7. C. Bonanno, P. Giulietti, M. Lenci, “Infinite mixing for one-dimensional maps with an indifferent fixed point”, Nonlinearity, 31:11 (2018), 5180–5213  crossref  mathscinet  zmath  isi  scopus
    8. V. V. Ryzhikov, “Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows”, Math. Notes, 104:6 (2018), 900–904  mathnet  crossref  crossref  mathscinet  isi  elib
    9. 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
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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