On a trace formula for functions of noncommuting operators

A. B. Aleksandrov; V. V. Peller; D. S. Potapov

On a trace formula for functions of noncommuting operators

Functional Analysis 2019-01-29 v1 Classical Analysis and ODEs Complex Variables Spectral Theory

Authors: A. B. Aleksandrov , V. V. Peller , D. S. Potapov

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 $(A_1,B_1)$ and $(A_2,B_2)$ of bounded self-adjoint operators with trace class differences $A_2-A_1$ and $B_2-B_1$ , it is impossible to estimate the modulus of the trace of the difference $f(A_2,B_2)-f(A_1,B_1)$ in terms of the norm of $f$ in the Lipschitz class.

Keywords

trace formula

Cite

@article{arxiv.1901.09495,
  title  = {On a trace formula for functions of noncommuting operators},
  author = {A. B. Aleksandrov and V. V. Peller and D. S. Potapov},
  journal= {arXiv preprint arXiv:1901.09495},
  year   = {2019}
}

Comments

8 pages

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