论文标题
耗散操作员的扰动对函数
Functons of perturbed pairs of dissipative operators
论文作者
论文摘要
令$ f $为不均匀的分析besov空间的功能$ b _ {\ infty，1}^1 $。对于一对$（l，m）的$不一定要通勤最大耗散操作员，我们将功能$ f（l，m）$ $ l $和$ m $定义为密集定义的线性运算符。 We prove for $p\in[1,2]$ that if $(L_1,M_1)$ and $(L_2,M_2)$ are pairs of not necessarily commuting maximal dissipative operators such that both differences $L_1-L_2$ and $M_1-M_2$ belong to the Schatten--von Neumann class $\boldsymbol{S}_p$ than for an arbitrary function $f$在不均匀的分析性besov空间中\ | f（l_1，m_1）-f（l_2，m_2）\ | _ {\ boldsymbol {s} _p} \ le \ operatorname {const} \ | f \ | _ {b _ {\ infty，1}^1} \ max \ max \ big \ big \ {\ | l_1-- l_2 \ | _ {\ boldsymbol {s} _p}，\ | m_1-m_2 \ | _ {\ boldsymbol {s} _p} _p} \ big \}。 $$
Let $f$ be a function in the inhomogeneous analytic Besov space $B_{\infty,1}^1$. For a pair $(L,M)$ of not necessarily commuting maximal dissipative operators, we define the function $f(L,M)$ of $L$ and $M$ as a densely defined linear operator. We prove for $p\in[1,2]$ that if $(L_1,M_1)$ and $(L_2,M_2)$ are pairs of not necessarily commuting maximal dissipative operators such that both differences $L_1-L_2$ and $M_1-M_2$ belong to the Schatten--von Neumann class $\boldsymbol{S}_p$ than for an arbitrary function $f$ in the inhomogeneous analytic Besov space $B_{\infty,1}^1$, the operator difference $f(L_1,M_1)-f(L_2,M_2)$ belongs to $\boldsymbol{S}_p$ and the following Lipschitz type estimate holds: $$ \|f(L_1,M_1)-f(L_2,M_2)\|_{\boldsymbol{S}_p} \le\operatorname{const}\|f\|_{B_{\infty,1}^1}\max\big\{\|L_1-L_2\|_{\boldsymbol{S}_p},\|M_1-M_2\|_{\boldsymbol{S}_p}\big\}. $$
