非交换算子在$\boldsymbol{S}_p$类扰动下的函数
Functions of noncommuting operators under perturbation of class $\boldsymbol{S}_p$
摘要：
本文证明了对于$p>2$，在齐次Besov类$B_{\infty,1}^1({\Bbb R}^2)$中存在自伴算子对$(A_1,B_1)$和$(A_2,B_2)$以及实直线上的函数$f$，使得$A_2-A_1$和$B_2-B_1$的差属于Schatten-von Neumann类$\boldsymbol{S}_p$而不属于$f(A_2,B_2)-f(A_1,B_1)\not\in\boldsymbol{S}_p$ .类似的结果也适用于压缩函数。对于任意$p\ge1$，我们还得到了自伴算子三元组情形下的类似结果
英文摘要：
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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