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The Behavior of Functions of Operators Under Perturbations

  • V. V. Peller
Part of the Operator Theory Advances and Applications book series (OT, volume 207)

Abstract

This is a survey article. We consider different problems in connection with the behavior of functions of operators under perturbations of operators. We deal with three classes of operators: unitary operators, self-adjoint operators, and contractions. We study operator Lipschitz and operator differentiable functions. We also study the behavior of functions under perturbations of an operator by an operator of Schatten-von Neumann class S p and apply the results to the Livschits—Krein and Koplienko—Neidhardt trace formulae. We also include in this survey article recent unexpected results obtained in a joint paper with Aleksandrov on operator Hölder—Zygmund functions.

Mathematics Subject Classification (2000)

47A55 47B10 47B35 47B15 46E15 

Keywords

Perturbation theory self-adjoint operator unitary operator contraction Lipschitz class operator Lipschitz functions Hölder classes Zygmund class Besov classes Hankel operators double operator integrals multiple operator integrals 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • V. V. Peller
    • 1
  1. 1.Mathematics DepartmentMichigan State UniversityEast LansingUSA

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