3×3阶上三角算子矩阵的四类点谱扰动

Pertubation of four classes of point spectra for 3 × 3 upper triangular operator matrices

基于值域的稠密性和闭性,有界线性算子的点谱可进一步细分为互不相交的四个组成部分,即四类点谱.设H_1,H_2,H_3为无穷维复可分Hilbert空间,记M_(D,E,F)=(A D E0 B F0 0 C)∈B(H_1H_2H_3).当对角算子A,B,C固定时,给出了M_(D,E,F)的四类点谱随D,E,F扰动的完全描述.

According to the denseness and the closedness of range, the point spectrum of a bounded linear operator is split into four disjoint parts, i.e., four classes of point spectra. Let H1, H2, H3 be infinite dimensional complex separable Hilbert spaces, and write MD,E,F= （A D E0 B F0 0 C）∈B（H_1⊕H_2⊕H_3）. Fixed the diagonal operators A ∈ B（H1）, B ∈ B（H2）, C ∈B（H3）, the perturbation descriptions of various point spectra for MD,E,F are given when D, E, F run over B（H2, H1）, B（H3, H1）,B（H3, H2）, respectively.