256 citations · 944 across the 58 of their papers we have counts for
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Double operator integral methods applied to continuity of spectral shift functions
Alan Carey, Fritz Gesztesy, Galina Levitina +3
We derive two main results: First, assume that , , , are self-adjoint operators in the Hilbert space , and suppose that converges to and $B_…
On the Index of a Non-Fredholm Model Operator
Alan Carey, Fritz Gesztesy, Galina Levitina +1
Let be a path of self-adjoint Fredholm operators in a Hilbert space , joining endpoints as . Computing the inde…
On Index Theory for Non-Fredholm Operators: A -Dimensional Example
Alan Carey, Fritz Gesztesy, Galina Levitina +3
Using the general formalism of [12], a study of index theory for non-Fredholm operators was initiated in [9]. Natural examples arise from -dimensional differential operators…
A noncommutative framework for topological insulators
Chris Bourne, Alan L. Carey, Adam Rennie
We study topological insulators, regarded as physical systems giving rise to topological invariants determined by symmetries both linear and anti-linear. Our perspective is that of…
The Spectral shift function and the Witten index
Alan Carey, Fritz Gesztesy, Galina Levitina +1
We survey the notion of the spectral shift function of a pair of self-adjoint operators and recent progress on its connection with the Witten index. We also describe a proof of Kre…
On a spectral flow formula for the homological index
Alan Carey, Harald Grosse, Jens Kaad
Consider a selfadjoint unbounded operator D on a Hilbert space H and a one parameter norm continuous family of selfadjoint bounded operators {A(t)} parametrized by the real line. T…