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Kato smoothness and functions of perturbed self-adjoint operators

Research output: Contribution to journalArticle

Rupert L. Frank, Alexander Pushnitski

Original languageEnglish
Pages (from-to)343-387
Number of pages45
JournalADVANCES IN MATHEMATICS
Volume351
Early online date20 May 2019
DOIs
Publication statusPublished - 31 Jul 2019

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Abstract

We consider the difference f(H1) - f(H0) for self-adjoint operators H0 and Hacting 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. As an important technical tool, we propose a new notion of Schatten class valued smoothness and develop a new framework for double operator integrals.

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