2×2分块对角算子矩阵拟谱的精细刻画

The Fine Pseudo-spectra of 2×2 Diagonal Block Operator Matrices

设A,B为可分Hilbert空间X中的稠定闭线性算子,M_(0)=(A00B)表示2×2分块算子矩阵.文中精细刻画算子矩阵M0在对角扰动情形下的拟点谱、拟剩余谱与拟连续谱,所得结论与点谱、剩余谱和连续谱的结果进行了比较,并用例子进行了辅证.最后,采用空间分解技巧,用主对角元的信息刻画M0在上三角扰动情形下的拟点谱分布.

Let A,B be densely closed linear operators in a separable Hilbert space X and M_(0)=(A00B) be the corresponding 2×2 block operator matrices.In this paper,we establish the fine 0 B pseudo-spectra of Mo including the pseudo-point spectrum,the pseudo-residual spectrum,and the pseudo-continuous spectrum under diagonal perturbation,which are,respectively,compared with its point spectrum,residual spectrum,and continuous spectrum.And a concrete example is constructed to justify the proved result.Finally,we obtain the pseudo-point spectrum of Mo under the upper-triangular perturbation by using the technology of space decomposition.