The spectral shift function and the Witten index

Authors

Alan L. Carey, Australian National University (ANU)
Fritz Gesztesy, University of Missouri
Galina Levitina, University of New South Wales (UNSW)
F Sukochev, University of New South Wales (UNSW), Flinders University

RIS ID

110450

Publication Details

Carey, A., Gesztesy, F., Levitina, G. & Sukochev, F. (2016). The spectral shift function and the Witten index. In M. Mantoiu, G. Raikov & R. Tiedra de. Aldecoa (Eds.), Spectral Theory and Mathematical Physics (pp. 71-105). Switzerland: Springer International.

Abstract

We survey the notion of the spectral shift function of two operators and recent progress on its connection with the Witten index. We begin with classical definitions of the spectral shift function E(.;H2,H1) under various assumptions on the pair of operators (H2,H1) in a fixed Hilbert space and then discuss some of its properties. We then present a new approach to defining the spectral shift function and discuss Krein's Trace Theorem.