Noncommutative Wiener-Wintner type ergodic theorems

TL;DR

This paper develops noncommutative ergodic theorems of Wiener-Wintner type using a noncommutative Banach principle, extending classical results to noncommutative settings with applications to positive Dunford-Schwartz operators.

Contribution

It introduces a noncommutative Banach principle for Wiener-Wintner results and establishes ergodic theorems for various weights in noncommutative spaces.

Findings

Proves noncommutative Wiener-Wintner ergodic theorems for weights in W1-space.

Analyzes b.a.u. and a.u. convergence of subsequential and moving averages.

Extends classical ergodic results to noncommutative operator frameworks.

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