Spectral theory of von Neumann algebra valued differential operators over non-compact manifolds

Abstract

We provide criteria for self-adjointness and $\tau$-Fredholmness 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.