  We provide criteria for self-adjointness and {\tau}-Fredhomness of first and
second order differential operators acting on sections of infinite dimensional
bundles, whose fibers are modules of finite type over a von Neumann algebra A
endowed with a trace {\tau}. We extend the Callias-type index to operators
acting on sections of such bundles and show that this index is stable under
compact perturbations.
