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Funktsional. Anal. i Prilozhen., 2000, Volume 34, Issue 4, Pages 1–17 (Mi faa322)  

This article is cited in 11 scientific papers (total in 11 papers)

Operator Ergodic Theorems for Actions of Free Semigroups and Groups

A. I. Bufetov

Independent University of Moscow

Abstract: New ergodic theorems are obtained for measure-preserving actions of free semigroups and groups. These theorems are derived from ergodic theorems for Markov operators. This approach also allows one to obtain ergodic theorems for some classes of Markov semigroups. Results of the paper generalize classical ergodic theorems of Kakutani, Oseledets, and Guivarc'h, and recent ergodic theorems of Grigorchuk, Nevo, and Nevo and Stein.

DOI: https://doi.org/10.4213/faa322

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English version:
Functional Analysis and Its Applications, 2000, 34:4, 239–251

Bibliographic databases:

UDC: 517.98
Received: 26.05.1999

Citation: A. I. Bufetov, “Operator Ergodic Theorems for Actions of Free Semigroups and Groups”, Funktsional. Anal. i Prilozhen., 34:4 (2000), 1–17; Funct. Anal. Appl., 34:4 (2000), 239–251

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Vershik, “Dynamic theory of growth in groups: Entropy, boundaries, examples”, Russian Math. Surveys, 55:4 (2000), 667–733  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. R. I. Grigorchuk, “An Ergodic Theorem for the Action of a Free Semigroup”, Proc. Steklov Inst. Math., 231 (2000), 113–127  mathnet  mathscinet  zmath
    3. Bufetov, AI, “Convergence of spherical averages for actions of free groups”, Annals of Mathematics, 155:3 (2002), 929  crossref  mathscinet  zmath  isi  scopus
    4. Anantharaman-Delaroche, C, “On ergodic theorems for free group actions on noncommutative spaces”, Probability Theory and Related Fields, 135:4 (2006), 520  crossref  mathscinet  zmath  isi  scopus
    5. G. Ya. Grabarnik, A. A. Katz, L. A. Shwartz, “On non-commutative ergodic type theorems for free finitely generated semigroups”, Vladikavk. matem. zhurn., 9:1 (2007), 38–47  mathnet  mathscinet  elib
    6. A. I. Bufetov, A. V. Klimenko, “Maximal inequality and ergodic theorems for Markov groups”, Proc. Steklov Inst. Math., 277 (2012), 27–42  mathnet  crossref  mathscinet  isi  elib  elib
    7. Bufetov A., Klimenko A., “On Markov Operators and Ergodic Theorems for Group Actions”, Eur. J. Comb., 33:7, SI (2012), 1427–1443  crossref  mathscinet  zmath  isi  elib  scopus
    8. Bufetov A.I., Khristoforov M., Klimenko A., “Cesaro Convergence of Spherical Averages for Measure-Preserving Actions of Markov Semigroups and Groups”, Int. Math. Res. Notices, 2012, no. 21, 4797–4829  crossref  mathscinet  zmath  isi  elib  scopus
    9. Bowen L., Nevo A., “Von Neumann and Birkhoff Ergodic Theorems For Negatively Curved Groups”, Ann. Sci. Ec. Norm. Super., 48:5 (2015), 1113–1147  crossref  mathscinet  zmath  isi
    10. Bowen L., Bufetov A., Romaskevich O., “Mean convergence of Markovian spherical averages for measure-preserving actions of the free group”, Geod. Dedic., 181:1 (2016), 293–306  crossref  mathscinet  zmath  isi  scopus
    11. Rahimi M., “Entropy of Action of Semi-Groups”, Iran. J. Sci. Technol. Trans. A-Sci., 41:A1 (2017), 179–183  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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