Standard

Operator Lipschitz functions. / Peller, V. V.; Александров, Алексей Борисович.

In: Russian Mathematical Surveys, Vol. 71, No. 4, 2016, p. 605-702.

Research output: Contribution to journal › Review article › peer-review

Harvard

Peller, VV & Александров, АБ 2016, 'Operator Lipschitz functions', Russian Mathematical Surveys, vol. 71, no. 4, pp. 605-702. https://doi.org/10.1070/RM9729

APA

Peller, V. V., & Александров, А. Б. (2016). Operator Lipschitz functions. Russian Mathematical Surveys, 71(4), 605-702. https://doi.org/10.1070/RM9729

Vancouver

Peller VV, Александров АБ. Operator Lipschitz functions. Russian Mathematical Surveys. 2016;71(4):605-702. https://doi.org/10.1070/RM9729

Author

Peller, V. V. ; Александров, Алексей Борисович. / Operator Lipschitz functions. In: Russian Mathematical Surveys. 2016 ; Vol. 71, No. 4. pp. 605-702.

BibTeX

@article{89b561dfc58245d68a9e68967d58f207,
title = "Operator Lipschitz functions",
abstract = "The goal of this survey is a comprehensive study of operator Lipschitz functions. A continuous function f on the real line R is said to be operator Lipschitz if ||f(A) - f(B)|| 6 const||A - B|| for arbitrary self-adjoint operators A and B. Sufficient conditions and necessary conditions are given for operator Lipschitzness. The class of operator differentiable functions on R is also studied. Further, operator Lipschitz functions on closed subsets of the plane are considered, and the class of commutator Lipschitz functions on such subsets is introduced. An important role for the study of such classes of functions is played by double operator integrals and Schur multipliers.",
keywords = "Besov classes, Carleson measures, Divided differences, Double operator integrals, Functions of operators, Linear-fractional transformations, Normal operators, Operator differentiable functions, Operator Lipschitz functions, Schur multipliers, Self-adjoint operators",
author = "Peller, {V. V.} and Александров, {Алексей Борисович}",
note = "Publisher Copyright: {\textcopyright} 2016 Russian Academy of Sciences ( DoM), London Mathematical Society, Turpion Ltd.",
year = "2016",
doi = "10.1070/RM9729",
language = "English",
volume = "71",
pages = "605--702",
journal = "Russian Mathematical Surveys",
issn = "0036-0279",
publisher = "IOP Publishing Ltd.",
number = "4",

}

RIS

TY - JOUR

T1 - Operator Lipschitz functions

AU - Peller, V. V.

AU - Александров, Алексей Борисович

N1 - Publisher Copyright: © 2016 Russian Academy of Sciences ( DoM), London Mathematical Society, Turpion Ltd.

PY - 2016

Y1 - 2016

N2 - The goal of this survey is a comprehensive study of operator Lipschitz functions. A continuous function f on the real line R is said to be operator Lipschitz if ||f(A) - f(B)|| 6 const||A - B|| for arbitrary self-adjoint operators A and B. Sufficient conditions and necessary conditions are given for operator Lipschitzness. The class of operator differentiable functions on R is also studied. Further, operator Lipschitz functions on closed subsets of the plane are considered, and the class of commutator Lipschitz functions on such subsets is introduced. An important role for the study of such classes of functions is played by double operator integrals and Schur multipliers.

AB - The goal of this survey is a comprehensive study of operator Lipschitz functions. A continuous function f on the real line R is said to be operator Lipschitz if ||f(A) - f(B)|| 6 const||A - B|| for arbitrary self-adjoint operators A and B. Sufficient conditions and necessary conditions are given for operator Lipschitzness. The class of operator differentiable functions on R is also studied. Further, operator Lipschitz functions on closed subsets of the plane are considered, and the class of commutator Lipschitz functions on such subsets is introduced. An important role for the study of such classes of functions is played by double operator integrals and Schur multipliers.

KW - Besov classes

KW - Carleson measures

KW - Divided differences

KW - Double operator integrals

KW - Functions of operators

KW - Linear-fractional transformations

KW - Normal operators

KW - Operator differentiable functions

KW - Operator Lipschitz functions

KW - Schur multipliers

KW - Self-adjoint operators

UR - http://www.scopus.com/inward/record.url?scp=84997294324&partnerID=8YFLogxK

U2 - 10.1070/RM9729

DO - 10.1070/RM9729

M3 - Review article

AN - SCOPUS:84997294324

VL - 71

SP - 605

EP - 702

JO - Russian Mathematical Surveys

JF - Russian Mathematical Surveys

SN - 0036-0279

IS - 4

ER -

ID: 87315155