Triple operator integrals in Schatten-von Neumann norms and functions of perturbed noncommuting operators

摘要

We study perturbations of functions f (A, B) of noncommuting self-adjoint operators A and B that can be defined in terms of double operator integrals. We prove that if f belongs to the Besov class B-infinity,1(1) (R-2), then we have the following Lipschitz-type estimate in the Schattenv-on Neumann norm S-p, 1 <= p <= 2: parallel to f(A(1), B-1) - f(A(2), B-2)parallel to S-p <= const(parallel to A(2) - A(1)parallel to S-p + parallel to B-1 - B-2 parallel to S-p). However, the condition f is an element of B-infinity,1(1) (R-2) does not imply the Lipschitz-type estimate in S-p with p > 2. The main tool is Schatten-von Neumann norm estimates for triple operator integrals. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.