2015/03/10 by Maxim Braverman, Braverman, Maxim, S. Cecchini +2
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Operator Algebras (math.OA) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.DG #math.OA #math.SP
paper · pdf · doi:10.48550/arxiv.1503.02998
15 pages. Final version, to appear in Journal of Noncommutative Geometry
openalex publication_date 2015/03/10 · arxiv created 2015/11/30 · arxiv updated 2015/12/01 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
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.