一类缺项算子矩阵的四类点谱的扰动

有界线性算子的点谱可进一步细分为4类,分别为$\sigma_{p1}$, $\sigma_{p2}$, $\sigma_{p3}$ 和$\sigma_{p4}$.设 $H, K$为无穷维可分的Hilbert空间,用$M_C$表示$2\times 2$上三角算子矩阵$\left(\begin{array}{cc} A & C \\ 0 & B \\ \end{array} \right)$,对于给定的 $A\in B(H),~B\in B(K)$,描述了集合$\bigcap\limits_{C\in B(K,H)}\sigma_{p1}(M_C)$, $\bigcap\limits_{C\in B(K,H)}\sigma_{p2}(M_C)$, $\bigcap\limits_{C\in B(K,H)}\sigma_{p3}(M_C)$和$\bigcap\limits_{C\in B(K,H)}\sigma_{p4}(M_C)$.

PERTURBATION OF FOUR KINDS OF POINT SPECTRUMS OF A CLASS OF UPPER TRIANGULAR OPERATOR MATRICES

The point spectrum is divided into four kinds $\sigma_{p1}$, $\sigma_{p2}$, $\sigma_{p3}$ and $\sigma_{p4}$. In this paper, let $H$ and $K$ be two separable Hilbert spaces. Donote by $M_C$ the $2\times 2$ upper triangular operator matrix acting on $H\oplus K $ of the form $\left(\begin{array}{cc} A & C\\ 0 & B\end{array}\right)$.For given operators $A\in B(H)$ and $B\in B(K)$, the sets $\bigcap\limits_{C\in B(K,H)}\sigma_{p1}(M_C)$, $\bigcap\limits_{C\in B(K,H)}\sigma_{p2}(M_C)$, $\bigcap\limits_{C\in B(K,H)}\sigma_{p3}(M_C)$ and $\bigcap\limits_{C\in B(K,H)}\sigma_{p4}(M_C)$ are characterized.