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Intégrales triples opératorielles en normes de Schatten-von Neumann et fonctions d'opérateurs perturbés ne commutant pas. / Александров, Алексей Борисович; Nazarov, Fedor; Peller, Vladimir.
в: Comptes Rendus Mathematique, Том 353, № 8, 2015, стр. 723-728.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Intégrales triples opératorielles en normes de Schatten-von Neumann et fonctions d'opérateurs perturbés ne commutant pas
AU - Александров, Алексей Борисович
AU - Nazarov, Fedor
AU - Peller, Vladimir
N1 - Funding Information: The research of the first author is partially supported by RFBR grant No. 14-01-00198 , the research of the second author is partially supported by NSF grant No. DMS 126562 , the research of the third author is partially supported by NSF grant No. DMS 1300924 . Publisher Copyright: © 2015 Académie des sciences. Published by Elsevier Masson SAS.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85027947773&partnerID=8YFLogxK
U2 - 10.1016/j.crma.2015.05.005
DO - 10.1016/j.crma.2015.05.005
M3 - статья
AN - SCOPUS:85027947773
VL - 353
SP - 723
EP - 728
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
SN - 1631-073X
IS - 8
ER -
ID: 87316856