Stochastic Banach principle in operator algebras
Volume 180 / 2007
Studia Mathematica 180 (2007), 255-270
MSC: Primary 46L51; Secondary 37A30.
DOI: 10.4064/sm180-3-5
Abstract
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.
