  For the Weyl-Heisenberg group, convolutions between functions and operators
were defined by Werner as a part of a framework called quantum harmonic
analysis. We show how recent results by Feichtinger can be used to extend this
definition to include convolutions between measures and operators. Many
properties of function-operator convolutions carry over to this setting and
allow us to prove novel results on the distribution of eigenvalues of
mixed-state Gabor multipliers and derive a version of the Berezin-Lieb
inequality for lattices. New results on the continuity of Gabor multipliers
with respect to lattice parameters, masks and windows as well as their ability
to approximate localization operators are also derived using this framework.
