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arXiv · 1601.00490

The Lifshits--Krein trace formula and operator Lipschitz functions

Vladmir Peller
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Abstract

We describe the maximal class of functions $f$ on the real line, for which the Lifshitz--Krein trace formula $\operatorname{trace}(f(A)-f(B))=\int_{\Bbb R} f'(s)\boldsymbolξ(s)\,ds$ holds for arbitrary self-adjoint operators $A$ and $B$ with $A-B$ in the trace class $\boldsymbol{S}_1$. We prove that this class of functions coincide with the class of operator Lipschitz functions.

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Vladmir Peller. 2016-01-04. The Lifshits--Krein trace formula and operator Lipschitz functions. https://arxiv.org/abs/1601.00490

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