On the index of a non-Fredholm model operator

Authors

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

RIS ID

111342

Publication Details

Carey, A., Gesztesy, F., Levitina, G. & Sukochev, F. (2016). On the index of a non-Fredholm model operator. Operators and Matrices, 10 (4), 881-914.

Abstract

Let {A(t)}t∈R be a path of self-adjoint Fredholm operators in a Hilbert space H , joining endpoints A± as t → ±∞. Computing the index of the operator DA = ∂ /∂ t + A acting on L2(R;H ), where A denotes the multiplication operator (A f)(t) = A(t) f (t) for f ∈ L2(R;H ) , and its relation to spectral flow along this path, has a long history, but it is mostly focussed on the case where the operators A(t) all have purely discrete spectrum.