The behavior of functions of operators under perturbations

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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 $\bS_p$ 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.
37 pages

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Functional Analysis, Classical Analysis and ODEs, Complex Variables, Spectral Theory, 47A55, 47B49, 47A60

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http://salesiana.dossiersoluciones.com/handle/123456789/226731

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0904.1761
 http://arxiv.org/abs/0904.1761

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arXiv