Mean lower bounds for Markov operators

Eduard Emel'yanov; Manfred Wolff

Annales Polonici Mathematici, Tome 83 (2004), p. 11-19 / Harvested from The Polish Digital Mathematics Library

Résumé

Let T be a Markov operator on an L¹-space. We study conditions under which T is mean ergodic and satisfies dim Fix(T) < ∞. Among other things we prove that the sequence $(n^{- 1} \sum_{k = 0}^{n - 1} T^{k}) ₙ$ converges strongly to a rank-one projection if and only if there exists a function 0 ≠ h ∈ L¹₊ which satisfies $l i m_{n \to \infty} | | (h - n^{- 1} \sum_{k = 0}^{n - 1} T^{k} f) ₊ | | = 0$ for every density f. Analogous results for strongly continuous semigroups are given.

Publié le : 2004-01-01

Zbl 1053.37002

EUDML-ID : urn:eudml:doc:281018

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     title = {Mean lower bounds for Markov operators},
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     year = {2004},
     pages = {11-19},
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Eduard Emel'yanov; Manfred Wolff. Mean lower bounds for Markov operators. Annales Polonici Mathematici, Tome 83 (2004) pp. 11-19. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-1-2/