MOORE-PENROSE SPECTRUMS OF 2×2 UPPER TRIANGULAR OPERATOR MATRICES
2×2阶上三角型算子矩阵的Moore-Penrose谱

Let $H_{1}$ and $H_{2}$ be infinite dimensional separable Hilbertspaces. Denote by $M_{C}$ the 2$\times$2 upper triangularoperator matrix acting on $H_{1}\oplus H_{2}$ of the form $\left(\begin{array}{cc} A & C \\ 0 & B \\\end{array}\right)$. For given operators $A\in{\mathcal{B}}(H_{1})$ and $B\in{\mathcal{B}}(H_{2})$, the sets $\bigcap\limits_{C\in{\mathcal{B}}(H_{2},H_{1})}\!\!\!\sigma_{M}(M_{C})$ and$\bigcup\limits_{C\in{\mathcal{B}}(H_{2},H_{1})}\!\!\!\sigma_{M}(M_{C})$ are characterized,where $\sigma_{M}(\cdot)$ denotes the Moore-Penrose spectrum.