Functons of perturbed pairs of dissipative operators (2201.07278v1)

Abstract: 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: $$ |f(L_1,M_1)-f(L_2,M_2)|{\boldsymbol{S}p} \le\operatorname{const}|f|{B_{\infty,1}^1}\max\big{|L_1-L_2|{\boldsymbol{S}_p},|M_1-M_2|{\boldsymbol{S}_p}\big}. $$