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arXiv · 1509.00616

Peller's problem concerning Koplienko-Neidhardt trace formulae: the unitary case

Clément Coine·Christian Le Merdy·Denis Potapov·Fedor Sukochev·Anna Tomskova
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Abstract

We prove the existence of a complex valued $C^2$-function on the unit circle, a unitary operator U and a self-adjoint operator Z in the Hilbert-Schmidt class $S^2$, such that the perturbated operator $$ f(e^{iZ}U)-f(U) -\frac{d}{dt}\bigl(f(e^{itZ}U)\bigr)_{\vert t=0} $$ does not belong to the space $S^1$ of trace class operators. This resolves a problem of Peller concerning the validity of the Koplienko-Neidhardt trace formula for unitaries.

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Clément Coine, Christian Le Merdy, Denis Potapov, Fedor Sukochev, Anna Tomskova. 2015-09-02. Peller's problem concerning Koplienko-Neidhardt trace formulae: the unitary case. https://arxiv.org/abs/1509.00616

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