The classical Banach principle is an essential tool for the investigation of ergodic properties of Cesàro subsequences. The aim of this work is to extend the Banach principle to the case of stochastic convergence in operator algebras. We start by establishing a sufficient condition for stochastic convergence (stochastic Banach principle). Then we prove stochastic convergence for bounded Besicovitch sequences, and as a consequence for uniform subsequences.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-3-5,
author = {Genady Ya. Grabarnik and Laura Shwartz},
title = {Stochastic Banach principle in operator algebras},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {255-270},
zbl = {1126.46041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-3-5}
}
Genady Ya. Grabarnik; Laura Shwartz. Stochastic Banach principle in operator algebras. Studia Mathematica, Tome 178 (2007) pp. 255-270. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-3-5/