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1996 | 121 | 1 | 67-85
Tytuł artykułu

On the uniform ergodic theorem in Banach spaces that do not contain duals

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let T be a power-bounded linear operator in a real Banach space X. We study the equality (*) $(I-T)X = {z ∈ X: sup_{n} ∥∑_{k=0}^{n} T^{k}z∥ < ∞}$. For X separable, we show that if T satisfies and is not uniformly ergodic, then $\overline{(I-T)X}$ contains an isomorphic copy of an infinite-dimensional dual Banach space. Consequently, if X is separable and does not contain isomorphic copies of infinite-dimensional dual Banach spaces, then (*) is equivalent to uniform ergodicity. As an application, sufficient conditions for uniform ergodicity of irreducible Markov chains on the (positive) integers are obtained.
Słowa kluczowe
Czasopismo
Rocznik
Tom
121
Numer
1
Strony
67-85
Opis fizyczny
Daty
wydano
1996
otrzymano
1996-02-26
poprawiono
1996-04-26
Twórcy
  • Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel, fonf@math.bgu.ac.il
autor
  • Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel, lin@math.bgu.ac.il
  • Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel, rubinov@math.bgu.ac.il
Bibliografia
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  • [BrSu_1] A. Brunel et L. Sucheston, Sur quelques conditions équivalentes à la super-reflexivité dans les espaces de Banach, C. R. Acad. Sci. Paris Sér. A 275 (1972), 993-994.
  • [BrSu_2] A. Brunel et L. Sucheston, On B-convex Banach spaces, Math. Systems Theory 7 (1974), 294-299.
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  • [L_1] M. Lin, On quasi-compact Markov operators, Ann. of Probab. 2 (1974), 464-475.
  • [L_2] M. Lin, On the uniform ergodic theorem, Proc. Amer. Math. Soc. 43 (1974), 337-340.
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  • [LS] M. Lin and R. Sine, Ergodic theory and the functional equation (I-T)x=y, J. Operator Theory 10 (1983), 153-166.
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  • [Z] R. Zaharopol, Mean ergodicity of power-bounded operators in countably order complete Banach lattices, Math. Z. 192 (1986), 81-88.
Typ dokumentu
Bibliografia
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