Email this article On a Trace Formula for Functions of Noncommuting Operators
- Authors: Aleksandrov A.B.1, Peller V.V.2,3, Potapov D.S.4
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Affiliations:
- St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
- Department of Mathematics
- RUDN University
- School of Mathematics and Statistics
- Issue: Vol 106, No 3-4 (2019)
- Pages: 481-487
- Section: Article
- URL: https://journals.rcsi.science/0001-4346/article/view/152079
- DOI: https://doi.org/10.1134/S0001434619090189
- ID: 152079
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Abstract
The main result of the paper is that the Lifshits-Krein trace formula cannot be generalized to the case of functions of noncommuting self-adjoint operators. To prove this, we show that, for pairs (A1, B1) and (A2, B2) of bounded self-adjoint operators with trace class differences A2-A1 and B2-B1, it is impossible to estimate the modulus of the trace of the difference f (A2, B2) - f (A1, B1) in terms of the norm of f in the Lipschitz class.
About the authors
A. B. Aleksandrov
St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
Author for correspondence.
Email: aall54eexx@gmail.com
Russian Federation, St. Petersburg, 191023
V. V. Peller
Department of Mathematics; RUDN University
Author for correspondence.
Email: peller@math.msu.edu
United States, East Lansing, MI, 48824; Moscow, 117198
D. S. Potapov
School of Mathematics and Statistics
Author for correspondence.
Email: d.potapov@unsw.edu.au
Australia, Kensington, NSW, 2052
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