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Frank, Rupert L.; Pushnitski, Alexander (2019): Kato smoothness and functions of perturbed self-adjoint operators. In: Advances in Mathematics, Vol. 351: pp. 343-387
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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. As an important technical tool, we propose a new notion of Schatten class valued smoothness and develop a new framework for double operator integrals. (C) 2019 Elsevier Inc. All rights reserved.