  We investigate the $\tau$-quantizations and Cohen's class distributions of a
suitable class of trace-class operators, called Feichtinger's operators, and
show that it is a convenient substitute for the class of Schwartz operators.
Many well-known concepts and results for functions in time-frequency analysis
have an operator-analog in our setting, e.g. that Cohen's classes are
convolutions of Wigner functions with distributions or characterization of the
class of Schwartz operators as an intersection of weighted variants of the
class of Feichtinger operators.
