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On a Trace Formula for Functions of Noncommuting Operators
A. B. Aleksandrova, V. V. Pellerbc, D. S. Potapovd a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Michigan State University, Department of Mathematics
c Peoples' Friendship University of Russia, Moscow
d University of New South Wales
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, trace class operators, operators Lipschitz functions, Lifshits–Krein trace formula.
Received: 24.11.2018
Citation:
A. B. Aleksandrov, V. V. Peller, D. S. Potapov, “On a Trace Formula for Functions of Noncommuting Operators”, Mat. Zametki, 106:4 (2019), 483–490; Math. Notes, 106:4 (2019), 481–487
Linking options:
https://www.mathnet.ru/eng/mzm12259https://doi.org/10.4213/mzm12259 https://www.mathnet.ru/eng/mzm/v106/i4/p483
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