On multiparameter weighted ergodic theorem for noncommutative Lp-spaces

In the paper we consider T1,…,Td absolute contractions of von Neumann algebra M with normal, semifinite, faithful trace, and prove that for every bounded Besicovitch weight {a(k)}k∈Nd and every x∈Lp(M) (p>1) the averagesAN(x)=1|N|∑k=1Na(k)Tk(x) converge bilaterally almost uniformly in Lp(M).