Let $\mathcal{H}$ and $\mathcal{K}$ be complex infinite dimensional separable Hilbert spaces. For given operators $A\in \mathcal{B}(\mathcal{H})$ and $B\in \mathcal{B}(\mathcal{K})$, we provide necessary and sufficient conditions which make a $2\times 2$ upper triangular operator matrix $M_C=\left(\begin{array}{cc}A& C\\ 0& B\end{array}\right)$ a CFI operator for some (or every) $C\in \mathcal{B}(\mathcal{K}\mathcal{,}\mathcal{H})$.

中文翻译：

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CFI 上三角算子矩阵

让$\mathcal{H}$和$\mathcal{钾}$是复杂的无限维可分希尔伯特空间。对于给定的运营商$A\in \mathcal{乙}(\mathcal{H})$和$乙\in \mathcal{乙}(\mathcal{钾})$，我们提供必要和充分的条件，使$\mathrm{2个}\times \mathrm{2个}$上三角算子矩阵${米}_C=\left(\begin{array}{cc}A& C\\ 0& 乙\end{array}\right)$一些（或每个）的 CFI 操作员$C\in \mathcal{乙}(\mathcal{钾}\mathcal{,}\mathcal{H})$.