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## Colloquium Mathematicum

2000 | 84/85 | 2 | 515-520
Tytuł artykułu

### Support overlapping $L_{1}$ contractions and exact non-singular transformations

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let T be a positive linear contraction of $L_{1}$ of a σ-finite measure space (X,Σ,μ) which overlaps supports. In general, T need not be completely mixing, but it is in the following cases: (i) T is the Frobenius-Perron operator of a non-singular transformation ϕ (in which case complete mixing is equivalent to exactness of ϕ). (ii) T is a Harris recurrent operator. (iii) T is a convolution operator on a compact group. (iv) T is a convolution operator on a LCA group.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
515-520
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-09-22
Twórcy
autor
• Ben-Gurion University of the Negev, Beer-Sheva, Israel
Bibliografia
• [ALW] J. Aaronson, M. Lin, and B. Weiss, Mixing properties of Markov operators and ergodic transformations, and ergodicity of Cartesian products, Israel J. Math. 33 (1979), 198-224.
• [AkBo] M. Akcoglu and D. Boivin, Approximation of $L_{p}$-contractions by isometries, Canad. Math. Bull. 32 (1989), 360-364.
• [B] W. Bartoszek, Asymptotic periodicity of the iterates of positive contractions on Banach lattices, Studia Math. 91 (1988), 179-188.
• [BBr] W. Bartoszek and T. Brown, On Frobenius-Perron operators which overlap supports, Bull. Polish Acad. Sci. Math. 45 (1997), 17-24.
• [F] S. Foguel, The Ergodic Theory of Markov Processes, Van Nostrand Reinhold, New York, 1969.
• [IRe] A. Iwanik and R. Rębowski, Structure of mixing and category of complete mixing for stochastic operators, Ann. Polon. Math. 56 (1992), 232-242.
• [JOr] B. Jamison and S. Orey, Tail σ-fields of Markov processes recurrent in the sense of Harris, Z. Wahrsch. Verw. Gebiete 8 (1967), 41-48.
• [K] U. Krengel, Ergodic Theorems, de Gruyter, Berlin, 1985.
• [KL] U. Krengel and M. Lin, On the deterministic and asymptotic σ-algebras of a Markov operator, Canad. Math. Bull. 32 (1989), 64-73.
• [L] M. Lin, Mixing for Markov operators, Z. Wahrsch. Verw. Gebiete 19 (1971), 231-242.
• [OS] D. Ornstein and L. Sucheston, An operator theorem on $L_{1}$ convergence to zero with applications to Markov kernels, Ann. Math. Statist. 41 (1970), 1631-1639.
• [R] R. Rudnicki, On asymptotic stability and sweeping for Markov operators, Bull. Polish Acad. Sci. Math. 43 (1995), 245-262.
• [Z] R. Zaharopol, Strongly asymptotically stable Frobenius-Perron operators, Proc. Amer. Math. Soc., in press.
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Bibliografia
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