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

Abstract

We provide criteria for self-adjointness and τ-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 τ. We extend the Callias-type index to operators acting on sections of such bundles and show that this index is stable under compact perturbations.

arXiv comment15 pages. Final version, to appear in Journal of Noncommutative Geometry