Geodesic
On a Trace Formula for Functions of Noncommuting Operators
Matematičeskie zametki, Tome 106 (2019) no. 4, pp. 483-490

Voir la notice de l'article provenant de la source Math-Net.Ru

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, trace class operators, operators Lipschitz functions, Lifshits–Krein trace formula. 
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     title = {On a {Trace} {Formula} for {Functions} of {Noncommuting} {Operators}},
     journal = {Matemati\v{c}eskie zametki},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_4_a0/}
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A. B. Aleksandrov; V. V. Peller; D. S. Potapov. On a Trace Formula for Functions of Noncommuting Operators. Matematičeskie zametki, Tome 106 (2019) no. 4, pp. 483-490. http://geodesic.mathdoc.fr/item/MZM_2019_106_4_a0/