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Uniform ergodic theorems for Markov operators onC(X)

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References

  1. Alfsen, E.M.: Compact Convex Sets and Boundary Integrals. Berlin-Heidelberg-New York: Springer 1971

    Google Scholar 

  2. Ando, T.: Invariante Masse positiver Kontraktionen inC(X). Studia Math.31, 173–187 (1968)

    Google Scholar 

  3. Axmann, D.: Struktur- und Ergodentheorie irreduzibler Operatoren auf Banachverbänden. Dissertation. Tübingen 1980

  4. Chou, C.: Minimal sets and ergodic measures for βℕ/ℕ. Illinois J. Math.13, 777–788 (1969)

    Google Scholar 

  5. Doeblin, W.: Sur les propriétés asymptotiques de mouvements régis par certains types de chaînes simples. II. Bull. Math. Soc. Roumaine Sci.39–2, 3–61 (1937)

    Google Scholar 

  6. Doob, J.L.: Stochastic Processes. New York-London: Wiley 1953

    Google Scholar 

  7. Dunford, N., Schwartz, J.T.: Linear Operators. Part I: General Theory. New York: Wiley 1958

    Google Scholar 

  8. Horowitz, S.: Transition probabilities and contractions ofL∞. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete24, 263–274 (1972)

    Google Scholar 

  9. Jacobs, K.: Neuere Methoden und Ergebnisse der Ergodentheorie. Berlin-Göttingen-Heidelberg: Springer 1960

    Google Scholar 

  10. Karlin, S.: Positive operators. J. Math. Mech.8, 907–937 (1959)

    Google Scholar 

  11. Kryloff, N., Bogoliuboff, N.: Sur les probabilités en chaîne. C.R. Acad. Sci. (Paris)204, 1368–1389 (1937)

    Google Scholar 

  12. Lin, M.: Quasi-compactness and uniform ergodicity of Markov operators. Ann. Inst. H. Poincaré Sect. B11, 345–354 (1975)

    Google Scholar 

  13. Lin, M.: Quasi-compactness and uniform ergodicity of positive operators. Israel J. Math.29, 309–311 (1978)

    Google Scholar 

  14. Nagel, R.J.: Mittelergodische Halbruppen linearer Operatoren Ann. Inst. Fourier (Grenoble)23, 75–87 (1973)

    Google Scholar 

  15. Rosenblatt, M.: Markov Processes. Structure and Asymptotic Behavior. Berlin-Heidelberg-New York: Springer 1971

    Google Scholar 

  16. Rosenthal, H.P.: On relatively disjoint families of measures, with some applications to Banach space theory. Studia Math.37, 13–36 (1970)

    Google Scholar 

  17. Rudin, W.: Averages of continuous functions on compact spaces. Duke Math. J.25, 195–204 (1958)

    Google Scholar 

  18. Schaefer, H.H.: Spectraleigenschaften positiver linearer Operatoren. Math. Z.82, 303–313 (1963)

    Google Scholar 

  19. Schaefer, H.H.: Invariant ideals of positive operators inC(X). I. Illinois J. Math.11, 703–715 (1967)

    Google Scholar 

  20. Schaefer, H.H.: Invariant ideals of positive operators inC(X). II. Illinois J. Math.12, 525–538 (1968)

    Google Scholar 

  21. Schaefer, H.H.: Banach Lattices and Positive Operators. Berlin-Heidelberg-New York: Springer 1974

    Google Scholar 

  22. Seever, G.L.: Measures onF-spaces. Trans. Amer. Math. Soc.133, 267–280 (1968)

    Google Scholar 

  23. Yosida, K., Kakutani, S.: Operator-theoretical treatment of Markov process and mean ergodic theorem. Ann. of Math. (2)42, 188–228 (1941)

    Google Scholar 

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Lotz, H.P. Uniform ergodic theorems for Markov operators onC(X) . Math Z 178, 145–156 (1981). https://doi.org/10.1007/BF01262036

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