Functions of noncommuting operators under perturbation of class Sp

A. B. Aleksandrov and V. V. Peller

Mathematische Nachrichten, 2020, vol. 293, issue 5, 847-860

Abstract: In this article we prove that for p>2, there exist pairs of self‐adjoint operators (A1,B1) and (A2,B2) and a function f on the real line in the homogeneous Besov class B∞,11(R2) such that the differences A2−A1 and B2−B1 belong to the Schatten–von Neumann class Sp but f(A2,B2)−f(A1,B1)∉Sp. A similar result holds for functions of contractions. We also obtain an analog of this result in the case of triples of self‐adjoint operators for any p≥1.

Date: 2020
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