Index theory for non-Fredholm operators
Jens Kaad (University of Paris)
Tuesday 19th November, 2013 16:00-17:00 Maths 416
In the eighties, the investigation of an index theory for non-Fredholm
operators was initiated by Gesztesy-Simon and Carey-Pincus.
The generalized index is defined as a scaling limit at zero of a super
trace of resolvents and is thus tightly linked to Krein's spectral
shift function. In this talk I will show how this non-Fredholm index
theory is related to cyclic theory. This implies certain invariance
properties of the generalized index under perturbations.
I will also present a local formula for the scaling limit at infinity
in the case of Dirac-type operators on Euclidean space.
The talk is based on joint work with Alan Carey and Harald Grosse.