Journal of Operator Theory

Volume 53, Issue 2, 2 2 pp. 331-350.

A few remarks in non-commutative ergodic theory

Authors: Vladimir Chilin (1) Semyon Litvinov (2) and Adam Skalski (3)
Author institution: (1) Department of Mathematics, National University of Uzbekistan, Tashkent 700095, Uzbekistan (2) Department of Mathematics, Pennsylvania State University, Hazleton, PA 18202, USA (3) Department of Mathematics, University of \L\'od\'z, Banacha 22, \L\'od\'z 90--238, Poland

Summary: Individual ergodic theorems for free group actions and Besico\-vitch weighted ergodic averages are proved in the context of the bilateral almost uniform convergence in the $L^1$-space over a semifinite von Neumann algebra. Some properties of the non-commutative counterparts of the pointwise convergence and the convergence in measure are discussed.

Keywords: Von Neumann algebra, bilateral almost uniform convergence, individual ergodic theorem, free group action, Besicovitch weights.

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