We study perturbations of functions f(A, B)of noncommuting self-adjoint operators Aand Bthat can be defined in terms of double operator integrals. We prove that if fbelongs to the Besov class B1∞,1(ℝ2), then we have the following Lipschitz-type estimate in the Schatten-von Neumann norm Sp, 1 ≤ p ≤ 2: ∥f(A1, B1) -f(A2, B1)∥Sp ≤ const(∥A1-A2∥Sp+∥B1-B2∥Sp). However, the condition f ε B1∞,1(ℝ2)does not imply the Lipschitz-type estimate in Sp with p < 2. The main tool is Schatten-von Neumann norm estimates for triple operator integrals.
Translated title of the contribution | Triple operator integrals in Schatten-von Neumann norms and functions of perturbed noncommuting operators |
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Original language | French |
Pages (from-to) | 723-728 |
Number of pages | 6 |
Journal | Comptes Rendus Mathematique |
Volume | 353 |
Issue number | 8 |
DOIs | |
State | Published - 2015 |
Externally published | Yes |
ID: 87316856