Stochastic Banach principle in operator algebras

DOI10.4064/SM180-3-5zbMATH Open1126.46041arXivmath/0606487OpenAlexW2019771962MaRDI QIDQ5293345

Laura Shwartz, Genady Ya. Grabarnik

Publication date: 29 June 2007

Published in: Studia Mathematica (Search for Journal in Brave)

Abstract: Classical 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.

Full work available at URL: https://arxiv.org/abs/math/0606487

zbMATH Keywords

Banach principlestochastic convergencesemi-finite von Neumann algebranon-commutative ergodic theorems

Mathematics Subject Classification ID

Ergodic theory of linear operators (47A35) Noncommutative measure and integration (46L51) Ergodic theorems, spectral theory, Markov operators (37A30)

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