C-admissibility and analytic \(C\)-semigroups
This paper gives a uniqueness result for the solution of the operator equation \(AX-XB=CD\) in the case of \(A\) being the generator of an analytic \(C\)-regularized semigroup in a Banach space \(F\) and \(B\) being a closed linear operator in \(F\) with some further properties. When \(C=I\), the result was proved by \textit{Q. P. Vu} and \textit{E. Schüler} in [J. Differ. Equations 145, No. 2, 394--419 (1998; Zbl 0918.34059)].
scientific article; zbMATH DE number 5930968