  We study mixed-state localization operators from the perspective of Werner's
operator convolutions which allows us to extend known results from the rank-one
case to trace class operators. The idea of localizing a signal to a domain in
phase space is approached from various directions such as bounds on the
spreading function, probability densities associated to mixed-state
localization operators, positive operator valued measures, positive
correspondence rules and variants of Tauberian theorems for operator
translates. Our results include a rigorous treatment of multiwindow-STFT
filters and a characterization of mixed-state localization operators as
positive correspondence rules. Furthermore, we provide a description of the
Cohen class in terms of Werner's convolution of operators and deduce
consequences on positive Cohen class distributions, an uncertainty principle,
uniqueness and phase retrieval for general elements of Cohen's class.
