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 W1-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

Edit:v2 - 25 pages, changed the name of the article, made numerous improvements to most results, added a section on subsequential and moving averages, and added a better method of checking conditions of the operators, and added more examples