A condition equivalent to uniform ergodicity
Studia Mathematica, Tome 167 (2005) no. 3, pp. 215-218
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let $T$ be a linear operator on a Banach space $X$ with $\mathop {\rm sup}_n \| T^n/n^w\| \infty $ for some $0\le w 1$. We show that the following conditions are equivalent: (i) $n^{-1}\sum _{k=0}^{n-1} T^k$ converges uniformly; (ii) ${\rm cl}\, (I -T)X = \{ z \in X : \mathop {\rm lim}_n\sum _{k=1}^n { T^kz/k}\hbox { exists} \} $.
Keywords:
linear operator banach space mathop sup w infty following conditions equivalent sum n converges uniformly t mathop lim sum hbox exists
Affiliations des auteurs :
Maria Elena Becker 1
@article{10_4064_sm167_3_2,
author = {Maria Elena Becker},
title = {A condition equivalent to uniform ergodicity},
journal = {Studia Mathematica},
pages = {215--218},
publisher = {mathdoc},
volume = {167},
number = {3},
year = {2005},
doi = {10.4064/sm167-3-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm167-3-2/}
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Maria Elena Becker. A condition equivalent to uniform ergodicity. Studia Mathematica, Tome 167 (2005) no. 3, pp. 215-218. doi: 10.4064/sm167-3-2
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