We consider the difference f(H_1)−f(H_0) for self-adjoint operators H_0 and H_1 acting in a Hilbert space. We establish a new class of estimates for the operator norm and the Schatten class norms of this difference. Our estimates utilise ideas of scattering theory and involve conditions on H_0 and H_1 in terms of the Kato smoothness. They allow for a much wider class of functions f (including some unbounded ones) than previously available results do. As an example we consider the case where H_0=−Δ and H_1=−Δ+V are the free and the perturbed Schrödinger operators in L^2(R^d), and V is a real-valued short range potential.
The talk is based on joint work with A. Pushnitski