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stochastic operators; quasi-compact
We show that a stochastic operator acting on the Banach lattice $L^1(m)$ of all $m$-integrable functions on $(X,\,\Cal A)$ is quasi-compact if and only if it is uniformly smoothing (see the definition below).
[B1] Bartoszek W.: On quasi-compactness and invariant measures of Markov operators on $C(X)$. Bull. Acad. Polon. Sci. 34 (1986), 69-72. MR 0850316 | Zbl 0614.47030
[B2] Bartoszek W.: Asymptotic periodicity of the iterates of positive contractions on Banach lattices. Studia Math. XCI (1988), 179-188. MR 0985720
[B3] Bartoszek W.: On the asymptotic behaviour of iterates of positive linear operators. Die Suid-Afrikaanse Wiskundevereniging Mededelings 25:1 (1993), 48-78.
[K] Komorník J.: Asymptotic decomposition of smoothing positive operators. Acta Universitatis Carolinae (1989), 30:2 77-81. MR 1046450
[KL] Komorník J., Lasota A.: Asymptotic decomposition of Markov operators. Bull. Acad. Polon. Sci. 35 no. 5-6 (1987), 321-327. MR 0919219
[LM] Lasota A., Mackey M.C.: Probabilistic Properties of Deterministic Systems. Cambridge University Press, Cambridge, 1985. MR 0832868 | Zbl 0606.58002
[S] Sine R.: A mean ergodic theorem. Proc. Amer. Math. Soc. 24 (1970), 438-439. MR 0252605 | Zbl 0191.42204
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