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Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 1511–1535 | Cite as

Lifshitz–Kreĭn Trace Formula for Hirsch Functional Calculus on Banach Spaces

  • A. R. MirotinEmail author
Article
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Abstract

We give a simple definition of a spectral shift function for pairs of nonpositive operators on Banach spaces and prove trace formulas of Lifshitz–Kreĭn type for a perturbation of an operator monotonic (negative complete Bernstein) function of negative and nonpositive operators on Banach spaces induced by nuclear perturbation of an operator argument. The Lipschitzness of such functions is also investigated. The results may be regarded as a contribution to a perturbation theory for Hirsch functional calculus.

Keywords

Spectral shift function Lifshitz–Kreĭn trace formula Hirsch functional calculus Negative operator Banach space Perturbation determinant 

Mathematics Subject Classification

Primary 47A56 Secondary 47A55 47B10 47L20 

Notes

Acknowledgements

The author would like to express his sincere gratitude to the referee for his very helpful comments and suggestions.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Programming TechnologiesF. Skorina Gomel State UniversityGomelBelarus

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