The Lifshits--Krein trace formula and operator Lipschitz functions

Abstract

We describe the maximal class of functions $f$ on the real line, for which the Lifshitz--Krein trace formula $\mathrm{trace}(f(A)-f(B))={\int }_{\mathbb{R}}{f}^{\prime }(s)\mathbf{\xi }(s)ds$ holds for arbitrary self-adjoint operators $A$ and $B$ with $A-B$ in the trace class ${\mathbf{S}}_1$. We prove that this class of functions coincide with the class of operator Lipschitz functions.

9 pages

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• Operator Lipschitz Functions