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arXiv · 1902.06346

Functions of noncommuting operators under perturbation of class $\boldsymbol{S}_p$

Aleksei Aleksandrov·Vladimir Peller
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Abstract

In this article we prove that for $p>2$, there exist pairs of self-adjoint operators $(A_1,B_1)$ and $(A_2,B_2)$ and a function $f$ on the real line in the homogeneous Besov class $B_{\infty,1}^1({\Bbb R}^2)$ such that the differences $A_2-A_1$ and $B_2-B_1$ belong to the Schatten--von Neumann class $\boldsymbol{S}_p$ but $f(A_2,B_2)-f(A_1,B_1)\not\in\boldsymbol{S}_p$. A similar result holds for functions of contractions. We also obtain an analog of this result in the case of triples of self-adjoint operators for any $p\ge1$

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BibTeXRIS

Aleksei Aleksandrov, Vladimir Peller. 2019-02-17. Functions of noncommuting operators under perturbation of class $\boldsymbol{S}_p$. https://arxiv.org/abs/1902.06346

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