On noncommutative weighted local ergodic theorems

Details On noncommutative weighted local ergodic theorems On noncommutative weighted local ergodic theorems

2007-01-15

arxiv.org/abs/math/0701415v2

Periodica Math. Hungarica, 55(2007), 223--235

Mathematics

Operator Algebras

11 pages. submitted

Scientific paper

In the present paper we consider a von Neumann algebra M with a faithful normal semi-finite trace $\t$, and $\{\alpha_ t\} $ a strongly continuous extension to $L^p(M,\t)$ of a semigroup of absolute contractions on $L^1 (M,\tau)$. 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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