算子矩阵的广义Kato分解与SVEP
Generalized Kato Decomposition For Operator Matrices and SVEP
摘要：
本文证明了对于有界线性算子$T$，相应的广义Kato分解谱$σ_{gK}(T)$满足等式$σ_{gD}(T)=σ_{gK}(T)\cup (S(T)\cup S(T^*))$，其中$σ_{gD} (T ) $是$T$和$S(T )$的广义Drazin谱（分别为，$S(T^*)$是其中T（分别，$T^*$）无法进行SVEP。作为应用，给出了上三角算子矩阵的广义Kato分解谱是其对角元谱的并的充分条件。并给出了一些应用实例。
英文摘要：
In this paper, we show that for a bounded linear operator $T$, the corresponding generalized Kato decomposition spectrum $σ_{gK}(T)$ satisfies the equality $σ_{gD}(T)=σ_{gK}(T)\cup (S(T)\cup S(T^*))$ where $σ_{gD} (T ) $ is the generalized Drazin spectrum of $T$ and $S(T )$ (resp., $S(T^*)$ is the set where T (resp., $T^*$) fails to have SVEP. As application, we give sufficient conditions which assure that the generalized Kato decomposition spectrum of an upper triangular operator matrices is the union of its diagonal entries spectra. Moreover, some applications are given.
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