  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.
