

Functional analysis and its applications
March 23, 2017 10:30–11:50






Onesided convergence in noncommutative individual ergodic theorems
V. I. Chilin^{a}, S. N. Litvinov^{b} ^{a} National University of Uzbekistan named after M. Ulugbek, Tashkent
^{b} Pennsylvania State University, Department of Mathematics

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Abstract:
It is known that, for a positive DunfordSchwartz operator in a noncommutative $L^p$space, or, more generally, in a noncommutative Orlicz space, the corresponding ergodic averages converge bilaterally almost uniformly. We show that these averages converge almost uniformly in each noncommutative symmetric space $E$ such that $\mu_t(x) \to 0$ as $t \to 0$ for every $x \in E$, where $\mu_t(x)$ is a nonincreasing rearrangement of $x$.

