Some noncommutative subsequential weighted individual ergodic theorems

Abstract

This paper is devoted to studying individual ergodic theorems for subsequential weighted ergodic averages on the noncommutative [Formula: see text]-spaces associated to a semifinite von Neumann algebra [Formula: see text]. In particular, we establish the convergence of these averages along sequences with density one and certain types of block sequences with positive lower density, and we extend known results along uniform sequences in the sense of Brunel and Keane.