A condition equivalent to uniform ergodicity

Maria Elena Becker

Studia Mathematica, Tome 166 (2005), p. 215-218 / Harvested from The Polish Digital Mathematics Library

Résumé

Let T be a linear operator on a Banach space X with $s u p ₙ | | T ⁿ / n^{w} | | < \infty$ for some 0 ≤ w < 1. We show that the following conditions are equivalent: (i) $n^{- 1} \sum_{k = 0}^{n - 1} T^{k}$ converges uniformly; (ii) $c l (I - T) X = z \in X : l i m_{n} \sum_{k = 1}^{n} T^{k} z / k e x i s t s$ .

Publié le : 2005-01-01

Zbl 1067.47010

EUDML-ID : urn:eudml:doc:284579

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     title = {A condition equivalent to uniform ergodicity},
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     volume = {166},
     year = {2005},
     pages = {215-218},
     zbl = {1067.47010},
     language = {en},
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Maria Elena Becker. A condition equivalent to uniform ergodicity. Studia Mathematica, Tome 166 (2005) pp. 215-218. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm167-3-2/