41 citations · 153 across the 25 of their papers we have counts for
20 papers · 1 filter
Fuglede theorem for symmetric spaces of -measurable operators
Denis Potapov, Fedor Sukochev, Anna Tomskova +1
We extend the classical Fuglede commutativity theorem to the full scale of symmetrically normed operator ideals. Our main result provides a complete characterization: a symmetric i…
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…
On a trace formula for functions of noncommuting operators
A. B. Aleksandrov, V. V. Peller, D. S. Potapov
The main result of the paper is that the Lifshits--Krein trace formula cannot be generalized to the case of functions of noncommuting self-adjoint operators. To prove this, we show…
Singular traces and perturbation formulae of higher order
Denis Potapov, Fedor Sukochev, Aleksandr Usachev +1
Let be self-adjoint operators such that belongs to the weak trace class ideal. We prove higher order perturbation formula $$τ\big(f(H+V)-\sum_{j=0}^{n-1}\frac{1}{j!}\fra…
Peller's problem concerning Koplienko-Neidhardt trace formulae: the unitary case
Clément Coine, Christian Le Merdy, Denis Potapov +2
We prove the existence of a complex valued -function on the unit circle, a unitary operator U and a self-adjoint operator Z in the Hilbert-Schmidt class , such that the p…
Resolution of Peller's problem concerning Koplienko-Neidhardt trace formulae
Clément Coine, Christian Le Merdy, Denis Potapov +2
A formula for the norm of a bilinear Schur multiplier acting from the Cartesian product of two copies of the Hilbert-Schmidt classes into the trac…