On surjectivity and denseness of range of the operator \(A+CX\)
Summary: Motivated by a result of \textit{K. Takahashi} [Integral Equations Oper. Theory 21, No. 3, 355--361 (1995; Zbl 0824.47002)], in this paper we investigate the problems of characterization of all the pairs of operators \(A\in\mathcal{B}(\mathcal{H},\mathcal{K})\) and \(C\in\mathcal{B}(\mathcal{L},\mathcal{K})\) for which there exists some \(X\in\mathcal{B}(\mathcal{H},\mathcal{L})\) such that the operator \(A+CX\) is surjective/with dense range, for some \(X\in\mathcal{B}(\mathcal{H},\mathcal{K})\). We completely solve the former and give some partial results regarding the latter one.
scientific article; zbMATH DE number 6930086