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Functions of perturbed noncommuting self-adjoint operators. / Александров, Алексей Борисович; Nazarov, Fedor; Peller, Vladimir.

In: Comptes Rendus Mathematique, Vol. 353, No. 3, 01.03.2015, p. 209-214.

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

Harvard

Александров, АБ, Nazarov, F & Peller, V 2015, 'Functions of perturbed noncommuting self-adjoint operators', Comptes Rendus Mathematique, vol. 353, no. 3, pp. 209-214. https://doi.org/10.1016/j.crma.2014.12.005

APA

Александров, А. Б., Nazarov, F., & Peller, V. (2015). Functions of perturbed noncommuting self-adjoint operators. Comptes Rendus Mathematique, 353(3), 209-214. https://doi.org/10.1016/j.crma.2014.12.005

Vancouver

Александров АБ, Nazarov F, Peller V. Functions of perturbed noncommuting self-adjoint operators. Comptes Rendus Mathematique. 2015 Mar 1;353(3):209-214. https://doi.org/10.1016/j.crma.2014.12.005

Author

Александров, Алексей Борисович ; Nazarov, Fedor ; Peller, Vladimir. / Functions of perturbed noncommuting self-adjoint operators. In: Comptes Rendus Mathematique. 2015 ; Vol. 353, No. 3. pp. 209-214.

BibTeX

@article{230ca9c71c0f4076a459af15bbbf5d56,
title = "Functions of perturbed noncommuting self-adjoint operators",
abstract = "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: {norm of matrix}f(A1,B1)-f(A2,B2){norm of matrix}S1≤const({norm of matrix}A1-A2{norm of matrix}S1+{norm of matrix}B1-B2{norm of matrix}S1). However, the condition f∈B∞,11(R2) does not imply the Lipschitz-type estimate in the operator norm.",
author = "Александров, {Алексей Борисович} and Fedor Nazarov and Vladimir Peller",
note = "Publisher Copyright: {\textcopyright} 2014 Acad{\'e}mie des sciences.",
year = "2015",
month = mar,
day = "1",
doi = "10.1016/j.crma.2014.12.005",
language = "English",
volume = "353",
pages = "209--214",
journal = "Comptes Rendus Mathematique",
issn = "1631-073X",
publisher = "Elsevier",
number = "3",

}

RIS

TY - JOUR

T1 - Functions of perturbed noncommuting self-adjoint operators

AU - Александров, Алексей Борисович

AU - Nazarov, Fedor

AU - Peller, Vladimir

N1 - Publisher Copyright: © 2014 Académie des sciences.

PY - 2015/3/1

Y1 - 2015/3/1

N2 - 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: {norm of matrix}f(A1,B1)-f(A2,B2){norm of matrix}S1≤const({norm of matrix}A1-A2{norm of matrix}S1+{norm of matrix}B1-B2{norm of matrix}S1). However, the condition f∈B∞,11(R2) does not imply the Lipschitz-type estimate in the operator norm.

AB - 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: {norm of matrix}f(A1,B1)-f(A2,B2){norm of matrix}S1≤const({norm of matrix}A1-A2{norm of matrix}S1+{norm of matrix}B1-B2{norm of matrix}S1). However, the condition f∈B∞,11(R2) does not imply the Lipschitz-type estimate in the operator norm.

UR - http://www.scopus.com/inward/record.url?scp=84922838530&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2014.12.005

DO - 10.1016/j.crma.2014.12.005

M3 - Article

AN - SCOPUS:84922838530

VL - 353

SP - 209

EP - 214

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 3

ER -

ID: 87317248