On a Trace Formula for Functions of Noncommuting Operators
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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.
Keywordstrace 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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