Alexander Pushnitski (King's)

Kato smoothness and functions of self-adjoint operators

Abstract:
The topic of the talk is a new approach to estimates of the operator norm and Schatten norms of f(A)-f(B), where A and B are self-adjoint operators in a Hilbert space. This approach was developed in my recent joint work with Rupert Frank. It utilises ideas of scattering theory and involves conditions on A and B in terms of Kato smoothness. As an important technical tool, a new notion of Schatten class valued Kato smoothness is proposed and a new framework for double operator integrals is developed.