Mathematical Notes

, Volume 106, Issue 3–4, pp 481–487 | Cite as

On a Trace Formula for Functions of Noncommuting Operators

  • A. B. AleksandrovEmail author
  • V. V. PellerEmail author
  • D. S. PotapovEmail author


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.


trace trace class operators operators Lipschitz functions Lifshits-Krein trace formula 


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The research of the first author was supported in part by the Russian Foundation for Basic Research under grant 17-01-00607. The publication was prepared with the support of the “RUDN University Program 5-100.” The research of the third author was supported in part by ARC.


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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of SciencesSt. PetersburgRussia
  2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA
  3. 3.RUDN UniversityMoscowRussia
  4. 4.School of Mathematics and StatisticsUniversity of New South WalesKensingtonAustralia

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