  This article is devoted to studying individual ergodic theorems for
subsequential weighted ergodic averages on the noncommutative Lp-spaces
associated to a semifinite von Neumann algebra M. 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.
