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arXiv · 1007.2994

Trace formulae for perturbations of class $\bs{\bS_m}$

Alexei Aleksandrov·Vladimir Peller
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Abstract

We obtain general trace formulae in the case of perturbation of self-adjoint operators by self-adjoint operators of class $\bS_m$, where $m$ is a positive integer. In \cite{PSS} a trace formula for operator Taylor polynomials was obtained. This formula includes the Livshits--Krein trace formula in the case $m=1$ and the Koplienko trace formula in the case $m=2$. We establish most general trace formulae in the case of perturbation of Schatten--von Neumann class $\bS_m$. We also improve the trace formula obtained in \cite{PSS} for operator Taylor polynomials and prove it for arbitrary functions in he Besov space $B_{\be1}^m(\R)$. We consider several other special cases of our general trace formulae. In particular, we establish a trace formula for $m$th order operator differences.

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BibTeXRIS

Alexei Aleksandrov, Vladimir Peller. 2010-07-18. Trace formulae for perturbations of class $\bs{\bS_m}$. https://arxiv.org/abs/1007.2994

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