Functions of noncommuting operators under perturbation of class S p

In this article we prove that for p > 2 , there exist pairs of self‐adjoint operators ( A 1 , B 1 ) and ( A 2 , B 2 ) and a function f on the real line in the homogeneous Besov classB ∞ , 1 1 ( R 2 )such that the differencesA 2 − A 1andB 2 − B 1belong to the Schatten–von Neumann class S p but f ( A 2 , B 2 ) − f ( A 1 , B 1 ) ∉ S p . 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 .