论文标题
在扰动下，成对的无界非司法自我接合操作员的功能
Functions of pairs of unbounded noncommuting self-adjoint operators under perturbation
论文作者
论文摘要
对于一对$（a，b）的$不一定是有限的，不一定要通勤自动接合操作员，并且对于欧几里得空间上的功能$ f $ $ {\ bbb r}^2 $这些操作员是密集定义的操作员。我们考虑了在$ $（a，b）$的扰动下估算功能$ f（a，b）$的问题。 It is established that if $1\le p\le2$, and $(A_1,B_1)$ and $(A_2,B_2)$ are pairs of not necessarily bounded and not necessarily commuting self-adjoint operators such that the operators $A_1-A_2$ and $B_1-B_2$ belong to the Schatten--von Neumann class $\boldsymbol{S}_p$ with $ p \ in [1,2] $和$ f \ in B _ {\ infty，1}^1（{\ bbb r}^2）$，然后以下Lipschitz Type estimate保持：\ [\ [\ | f（a_1，b_1，b_1，b_1）-f（a_2，b_2，b_2，b_2） \ le \ operatorName {const} \ | f \ | _ {b _ {\ infty，1}^1} \ max \ big \ big \ \ {\ | a_1-- a_2 \ | _ {\ boldsymbol {s} _p}，\ | b_1-b_2 \ | _ {\ boldsymbol {s} _p} _p} \ big \}。 \]
For a pair $(A,B)$ of not necessarily bounded and not necessarily commuting self-adjoint operators and for a function $f$ on the Euclidean space ${\Bbb R}^2$ that belongs to the inhomogeneous Besov class $B_{\infty,1}^1({\Bbb R}^2)$, we define the function $f(A,B)$ of these operators as a densely defined operator. We consider the problem of estimating the functions $f(A,B)$ under perturbations of the pair $(A,B)$. It is established that if $1\le p\le2$, and $(A_1,B_1)$ and $(A_2,B_2)$ are pairs of not necessarily bounded and not necessarily commuting self-adjoint operators such that the operators $A_1-A_2$ and $B_1-B_2$ belong to the Schatten--von Neumann class $\boldsymbol{S}_p$ with $p\in[1,2]$ and $f\in B_{\infty,1}^1({\Bbb R}^2)$, then the following Lipschitz type estimate holds: \[ \|f(A_1,B_1)-f(A_2,B_2)\|_{\boldsymbol{S}_p} \le\operatorname{const}\|f\|_{B_{\infty,1}^1}\max\big\{\|A_1-A_2\|_{\boldsymbol{S}_p},\|B_1-B_2\|_{\boldsymbol{S}_p}\big\}. \]
