On multiparameter weighted ergodic theorem for noncommutative Lp-spaces

In the paper we consider T1, . . . , Td absolute contractions of von Neumann algebraMwith normal, semifinite, faithful trace, and prove that for every bounded Besicovitch weight {a(k)} k∈Nd and every x ∈ Lp(M) (p >1) the averages AN(x) = 1 |N| N k=1 a(k)Tk(x) converge bilaterally almost uniformly in Lp(M). © 2008 Elsevier Inc. All rights reserved.