2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113957Classical Banach principle is an essential tool for the investigation of the ergodic properties of Cesaro subsequences. The aim of this work is to extend Banach principle to the case of the stochastic convergence in the operator algebras. We start by establishing a sufficient condition for the stochastic convergence (stochastic Banach principle). Then we formulate stochastic convergence for the bounded Besicovitch sequences, and, as consequence for uniform subsequences.Operator AlgebrasDynamical SystemsPrimary 46L51; Secondary 37A30text