Resolution of Peller's problem concerning Koplienko-Neidhardt trace formulae (Q2827964)
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scientific article; zbMATH DE number 6642535
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Resolution of Peller's problem concerning Koplienko-Neidhardt trace formulae |
scientific article; zbMATH DE number 6642535 |
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24 October 2016
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Koplienko-Neidhardt trace formulae
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self-adjoint operators
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Hilbert-Schmidt class
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Resolution of Peller's problem concerning Koplienko-Neidhardt trace formulae (English)
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The main result of the article under review is a negative solution to the problem posed in [\textit{B. S. Pavlov}, Probl. Mat. Anal. 2, 99--122 (1969; Zbl 0211.17201)] on the validity of the Koplienko-Neidhardt trace formulae. Namely, the authors prove that there exist a \(C^2\) function \(f\) on the real line with bounded second derivative, a self-adjoint operator \(A\) and a Hilbert-Schmidt self-adjoint operator \(B\) such that the operator NEWLINE\[NEWLINE f(A+B)-f(A)-\frac{d}{dt}(A+tB)\Big|_{t=0} NEWLINE\]NEWLINE does not belong to the trace class.
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