Caltech/UCLA Joint Analysis Seminar

We consider the difference f(H1)−f(H0) for self-adjoint operators H0 and H1 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 H0 and H1 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 H0=−Δ and H1=−Δ+V are the free and the perturbed Schrödinger operators in L2(Rd), and V is a real-valued short range potential. The talk is based on joint work with A. Pushnitski