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On a Trace Formula for Functions of Noncommuting Operators. / Александров, Алексей Борисович; Peller, V. V.; Potapov, D. S.
в: Mathematical Notes, Том 106, № 3-4, 01.09.2019, стр. 481-487.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - On a Trace Formula for Functions of Noncommuting Operators
AU - Александров, Алексей Борисович
AU - Peller, V. V.
AU - Potapov, D. S.
N1 - Publisher Copyright: © 2019, Pleiades Publishing, Ltd.
PY - 2019/9/1
Y1 - 2019/9/1
N2 - 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.
AB - 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.
KW - Lifshits-Krein trace formula
KW - operators Lipschitz functions
KW - trace
KW - trace class operators
UR - http://www.scopus.com/inward/record.url?scp=85074101503&partnerID=8YFLogxK
U2 - 10.1134/S0001434619090189
DO - 10.1134/S0001434619090189
M3 - Article
AN - SCOPUS:85074101503
VL - 106
SP - 481
EP - 487
JO - Mathematical Notes
JF - Mathematical Notes
SN - 0001-4346
IS - 3-4
ER -
ID: 87314853