Uniform vector-valued pointwise ergodic theorems for operators

Abstract

We prove a uniform vector-valued Wiener-Wintner Theorem for a class of operators that includes compositions of ergodic Koopman operators with contractive multiplication operators. Our results are new even in the case of complex-valued functions, as they also apply to some non-positive non-contractive operators, and they give new uniform pointwise theorems for ergodic, weakly mixing, and mildly mixing Koopman operators.

This is the journal edition of the article, but the formatting is not the same, so it is 5 pages longer than the journal edition