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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2017, Vol. 32 Issue (1): 93-102    DOI:
    
Pertubation of four classes of point spectra for $3\times3$ upper triangular operator matrices
WU Xiu-feng1, HUANG Jun-jie1, Alatancang2
1. School of Math. Sci., Inner Mongolia Univ., Hohhot 010021, China
2. Dept. of Math. Sci., Hohhot Minzu College., Hohhot 010051, China
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Abstract  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 $\mathcal{H}_1,\mathcal{H}_2,\mathcal{H}_3$ be infinite dimensional complex separable Hilbert spaces, and write $M_{D,E,F}=\begin{pmatrix}A &D &E\\0 &B &F\\0 &0 &C\end{pmatrix}\in \mathcal{B}(\mathcal{H}_1\oplus\mathcal{H}_2\oplus\mathcal{H}_3)$. Fixed the diagonal operators $A\in \mathcal{B}(\mathcal{H}_1)$, $B\in \mathcal{B}(\mathcal{H}_2)$, $C\in \mathcal{B}(\mathcal{H}_3)$, the perturbation descriptions of various point spectra for $M_{D,E,F}$ are given when $D, E, F$ run over $\mathcal{B}(\mathcal{H}_2, \mathcal{H}_1)$, $\mathcal{B}(\mathcal{H}_3, \mathcal{H}_1)$, $\mathcal{B}(\mathcal{H}_3, \mathcal{H}_2)$, respectively.

Key words：  operator matrix      point spectrum      perturbation      
Received: 05 April 2016      Published: 18 March 2018
CLC:  O177.1  
  O177.7  
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WU Xiu-feng
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Alatancang
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WU Xiu-feng, HUANG Jun-jie, Alatancang. Pertubation of four classes of point spectra for $3\times3$ upper triangular operator matrices. Applied Mathematics A Journal of Chinese Universities, 2017, 32(1): 93-102.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2017/V32/I1/93


$3\times 3$阶上三角算子矩阵的四类点谱扰动

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$\mathcal{H}_1,\mathcal{H}_2,\mathcal{H}_3$为无穷维复可分Hilbert空间, 记$M_{D,E,F}=\begin{pmatrix}A &D &E\\0 &B &F\\0 &0 &C\end{pmatrix}\in \mathcal{B}(\mathcal{H}_1\oplus\mathcal{H}_2\oplus\mathcal{H}_3)$. 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.

关键词： 算子矩阵,  点谱,  扰动 
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