Результаты исследований: Научные публикации в периодических изданиях › Обзорная статья › Рецензирование
Operator Lipschitz functions. / Peller, V. V.; Александров, Алексей Борисович.
в: Russian Mathematical Surveys, Том 71, № 4, 2016, стр. 605-702.Результаты исследований: Научные публикации в периодических изданиях › Обзорная статья › Рецензирование
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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