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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.
Genady Ya. Grabarnik, and Laura Shwartz. "Stochastic Banach principle in operator algebras." Studia Mathematica 180.3 (2007): 255-270. <http://eudml.org/doc/284802>.
@article{GenadyYa2007, 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.}, author = {Genady Ya. Grabarnik, Laura Shwartz}, journal = {Studia Mathematica}, keywords = {Banach principle; semi-finite von Neumann algebra; non-commutative ergodic theorems; stochastic convergence}, language = {eng}, number = {3}, pages = {255-270}, title = {Stochastic Banach principle in operator algebras}, url = {http://eudml.org/doc/284802}, volume = {180}, year = {2007}, }
TY - JOUR AU - Genady Ya. Grabarnik AU - Laura Shwartz TI - Stochastic Banach principle in operator algebras JO - Studia Mathematica PY - 2007 VL - 180 IS - 3 SP - 255 EP - 270 AB - 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. LA - eng KW - Banach principle; semi-finite von Neumann algebra; non-commutative ergodic theorems; stochastic convergence UR - http://eudml.org/doc/284802 ER -