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On noncommutative weighted local ergodic theorems

Farrukh Mukhamedov·Abdusalom Karimov
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Abstract

In the present paper we consider a von Neumann algebra M with a faithful normal semi-finite trace $\t$, and $\{α_ t\} $ a strongly continuous extension to $L^p(M,\t)$ of a semigroup of absolute contractions on $L^1 (M,τ)$. By means of a non-commutative Banach Principle we prove for a Besicovitch function b and $x\in L^p(M,\t)$, the averages \frac{1}{T}\int_0^Tb(t)\a_t(x)dt converge bilateral almost uniform in $L^p(M,\t)$ as $T\to 0$.

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Farrukh Mukhamedov, Abdusalom Karimov. 2007-07-27. On noncommutative weighted local ergodic theorems. https://arxiv.org/abs/math/0701415

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