On noncommutative ergodic theorems for semigroup and free group actions

Abstract: In this article, we consider actions of \mathcal{Z}+^d, \mathcal{R}+^d and finitely generated free groups on a von Neumann algebras $M$ and prove a version of maximal ergodic inequality. Additionally, we establish non-commutative analogues of pointwise ergodic theorems for associated actions in the predual when M is finite.