Noncommutative Wiener–Wintner type ergodic theorems
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.