23 citations · 44 across the 9 of their papers we have counts for
13 papers
Analytic spectral flow formula for unitaries and Levinson's theorem
A. Alexander, A. Carey, G. Levitina +1
We prove an integral formula for the spectral flow of differentiable loops of unitaries of the form Schatten. Our formula is in terms of a regularised winding number, ex…
On a conjectured property of the Witten index and an application to Levinson's theorem
Alan Carey, Galina Levitina
A few years ago Fritz Gesztesy raised the issue of whether there was a composition rule for the Witten index analogous to that satisfied by Fredholm operators. In this note we prov…
The limiting absorption principle for massless Dirac operators, properties of spectral shift functions, and an application to the Witten index of non-Fredholm operators
Alan Carey, Fritz Gesztesy, Galina Levitina +3
We derive a limiting absorption principle on any compact interval in for the free massless Dirac operator, in $[L^2(\mathbb…
The Witten index and the spectral shift function
Alan Carey, Galina Levitina, Denis Potapov +1
In \cite{APSIII} Atiyah, Patodi and Singer introduced spectral flow for elliptic operators on odd dimensional compact manifolds. They argued that it could be computed from the Fred…
Pietsch correspondence for symmetric functionals on Calkin operator spaces associated with semifinite von Neumann algebras
Galina Levitina, Alexandr Usachev
In this paper we extend the Pietsch correspondence for ideals of compact operators and traces on them to the semifinite setting. We prove that a shift-monotone space of seq…
Noncommutative Geometry for Symmetric Non-Self-Adjoint Operators
Alain Connes, Galina Levitina, Edward McDonald +2
We introduce the notion of a pre-spectral triple, which is a generalisation of a spectral triple where is no longer required to be self-adjoint, but close…
On the Global Limiting Absorption Principle for Massless Dirac Operators
Alan Carey, Fritz Gesztesy, Jens Kaad +4
We prove a global limiting absorption principle on the entire real line for free, massless Dirac operators for all space dimensions , $…
Cwikel estimates revisited
Galina Levitina, Fedor Sukochev, Dmitriy Zanin
In this paper, we propose a new approach to Cwikel estimates both for the Euclidean space and for the noncommutative Euclidean space.
Trace Formulas for a Class of non-Fredholm Operators: A Review
Alan Carey, Fritz Gesztesy, Harald Grosse +4
We review previous work on spectral flow in connection with certain self-adjoint model operators on a Hilbert space , joining endpoints $A…
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…
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…