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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.

In: Comptes Rendus Mathematique, Vol. 353, No. 8, 2015, p. 723-728.

Research output: Contribution to journal › Article › peer-review

Harvard

Александров, АБ, Nazarov, F & Peller, V 2015, 'Intégrales triples opératorielles en normes de Schatten-von Neumann et fonctions d'opérateurs perturbés ne commutant pas', Comptes Rendus Mathematique, vol. 353, no. 8, pp. 723-728. https://doi.org/10.1016/j.crma.2015.05.005

APA

Александров, А. Б., Nazarov, F., & Peller, V. (2015). Intégrales triples opératorielles en normes de Schatten-von Neumann et fonctions d'opérateurs perturbés ne commutant pas. Comptes Rendus Mathematique, 353(8), 723-728. https://doi.org/10.1016/j.crma.2015.05.005

Vancouver

Александров АБ, Nazarov F, Peller V. Intégrales triples opératorielles en normes de Schatten-von Neumann et fonctions d'opérateurs perturbés ne commutant pas. Comptes Rendus Mathematique. 2015;353(8):723-728. https://doi.org/10.1016/j.crma.2015.05.005

Author

Александров, Алексей Борисович ; Nazarov, Fedor ; Peller, Vladimir. / Intégrales triples opératorielles en normes de Schatten-von Neumann et fonctions d'opérateurs perturbés ne commutant pas. In: Comptes Rendus Mathematique. 2015 ; Vol. 353, No. 8. pp. 723-728.

BibTeX

@article{d2cfc0410e2b4d929399c56f6ed70f2b,
title = "Int{\'e}grales triples op{\'e}ratorielles en normes de Schatten-von Neumann et fonctions d'op{\'e}rateurs perturb{\'e}s ne commutant pas",
abstract = "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.",
author = "Александров, {Алексей Борисович} and Fedor Nazarov and Vladimir Peller",
note = "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: {\textcopyright} 2015 Acad{\'e}mie des sciences. Published by Elsevier Masson SAS.",
year = "2015",
doi = "10.1016/j.crma.2015.05.005",
language = "французский",
volume = "353",
pages = "723--728",
journal = "Comptes Rendus Mathematique",
issn = "1631-073X",
publisher = "Elsevier",
number = "8",

}

RIS

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