Noncommutative Wiener–Wintner type ergodic theorems

Abstract

. In this article, we obtain a version of the noncommutative Banach Principle suitable to prove Wiener-Wintner type results for weights in W 1 space. This is used to obtain noncommutative Wiener-Wintner type ergodic theorems for various types of weights for certain types of positive Dunford-Schwartz operators. We also study the b.a.u. (a.u.) convergence of some subsequential averages and moving averages of such operators.