We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.
@article{bwmeta1.element.bwnjournal-article-smv141i3p201bwm,
author = {Teresa Berm\'udez and Manuel Gonz\'alez and Mostafa Mbekhta},
title = {Operators with an ergodic power},
journal = {Studia Mathematica},
volume = {141},
year = {2000},
pages = {201-208},
zbl = {0986.47006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv141i3p201bwm}
}
Bermúdez, Teresa; González, Manuel; Mbekhta, Mostafa. Operators with an ergodic power. Studia Mathematica, Tome 141 (2000) pp. 201-208. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv141i3p201bwm/
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