2×2阶上三角型算子矩阵的Moore-Penrose谱

设$H_{1}$和$H_{2}$是无穷维可分Hilbert空间. 用$M_{C}$表示$H_{1}oplusH_{2}$上的2$times$2阶上三角型算子矩阵$left(begin{array}{cc} A & C 0 & B end{array}right)$. 对给定的算子$Ain{mathcal{B}}(H_{1})$和$Bin{mathcal{B}}(H_{2})$,描述了集合$bigcaplimits_{Cin{mathcal{B}}(H_{2},H_{1})}!!!sigma_{M}(M_{C})$与$bigcuplimits_{Cin{mathcal{B}}(H_{2},H_{1})}!!!sigma_{M}(M_{C})$,其中$sigma_{M}(cdot)$表示Moore-Penrose谱.