Comptes Rendus
Mathematical analysis/Functional analysis
Functions of perturbed noncommuting self-adjoint operators
Comptes Rendus. Mathématique, Volume 353 (2015) no. 3, pp. 209-214.

We consider 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,11(R2), then we have the following Lipschitz-type estimate in the trace norm: f(A1,B1)f(A2,B2)S1const(A1A2S1+B1B2S1). However, the condition fB,11(R2) does not imply the Lipschitz-type estimate in the operator norm.

Nous considérons les fonctions f(A,B) d'opérateurs auto-adjoints A et B qui ne commutent pas. De telles fonctions peuvent être définies en termes d'intégrales doubles opératorielles. Pour f dans l'espace de Besov B,11(R2), nous obtenons l'estimation lipschitzienne en norme trace : f(A1,B1)f(A2,B2)S1const(A1A2S1+B1B2S1). Par ailleurs, la condition fB,11(R2) n'implique pas l'estimation lip-schitzienne en norme opératorielle.

Published online:
DOI: 10.1016/j.crma.2014.12.005

Aleksei Aleksandrov 1; Fedor Nazarov 2; Vladimir Peller 3

1 St-Petersburg Branch, Steklov Institute of Mathematics, Fontanka 27, 191023 St-Petersburg, Russia
2 Department of Mathematics, Kent State University, Kent, OH 44242, USA
3 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
     author = {Aleksei Aleksandrov and Fedor Nazarov and Vladimir Peller},
     title = {Functions of perturbed noncommuting self-adjoint operators},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {209--214},
     publisher = {Elsevier},
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     year = {2015},
     doi = {10.1016/j.crma.2014.12.005},
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%A Vladimir Peller
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Aleksei Aleksandrov; Fedor Nazarov; Vladimir Peller. Functions of perturbed noncommuting self-adjoint operators. Comptes Rendus. Mathématique, Volume 353 (2015) no. 3, pp. 209-214. doi : 10.1016/j.crma.2014.12.005.

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