关于某类2×2缺项算子矩阵的谱补

On the Spectral Completion of a Class of Operator Partial Matrices

对于Hilbert空间上的2×2缺项算子矩阵和，我们刻画了它们所有补的谱的交集与并集，也给出了缺项算式矩阵具有补T＝满足X和Y是紧算子使得σ（T）Ω的充分必要条件，其中Ω是复平面上包含零点的非空开集，且具有每个连通分支是单通的．这个结论也被应用于讨论连续（或离散）时间无限维线性系统的指数（或幂）稳定性问题．

The union and the intersection of the spectra of all completions of operator partial matrices of the form (? ?) and (D ?) with given operator A, C and D are completely characterized. A sufficient and necessary condition is given for an operator partial matrix { ? f) to have a completion T= (X Y) such that σ(T)n with X and Y being compact operators, where Ω is a given open set containing zero in the complex plan with every component being simply connected. This result is also used to discuss the exponential (or power) stabilizability of a continuous (or discrete) time infinite dimensional systems.