We provide criteria for self-adjointness and -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 endowed with a trace . We extend the Callias-type index to operators acting on sections of such bundles and show that this index is stable under compact perturbations.
Cite this article
Maxim Braverman, Simone Cecchini, Spectral theory of von Neumann algebra valued differential operators over non-compact manifolds. J. Noncommut. Geom. 10 (2016), no. 4, pp. 1589–1609DOI 10.4171/JNCG/267