Weighted Subsequential ergodic theorems on Orlicz spaces

Abstract

For a semifinite von Neumann algebra M, individual convergence of subsequential, \mathcal{Z}(M) (center of M) valued weighted ergodic averages are studied in noncommutative Orlicz spaces. In the process, we also derive a maximal ergodic inequality corresponding to such averages in noncommutative L^p~ (1 \leq p < \infty) spaces using the weak (1,1) inequality obtained by Yeadon.