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A functional calculus of closed operators on Banach space. III. certain topics of perturbation theory

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Abstract

The present paper is a continuation of research of A. A. Atvinovskii and of the author in the area of functional calculus of closed operators on Banach spaces based on Markov and related functions as symbols. The following topics in the perturbation theory are considered: Estimates of bounded perturbations of operator functions with respect to general operator ideal norms, Lipschitz property, moment inequality, Fréchet differentiability, analyticity of operator functions under consideration with respect to the perturbation parameter, spectral shift function, and Lifshits–Krein trace formula.

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Authors and Affiliations

  1. F. Skorina Gomel State University, ul. Sovetskaya 104, Gomel, 246019, Republic of Belarus

    A. R. Mirotin

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  1. A. R. Mirotin
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Correspondence to A. R. Mirotin.

Additional information

Original Russian Text © A.R. Mirotin, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 12, pp. 24–34.

The author is grateful to the referee who indicated to him this work.

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Mirotin, A.R. A functional calculus of closed operators on Banach space. III. certain topics of perturbation theory. Russ Math. 61, 19–28 (2017). https://doi.org/10.3103/S1066369X17120039

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