【摘要】 <正> 本文从谱约化的角度讨论Banach空间上的闭可约化算子,闭谱算子及闭可分解算子的谱特征,并研究了这三类算子间的关系,最后给出Banach空间上一个闭线性算子成为闭谱算子的充分必要条件。设C表示复平面,C_∞表示扩充复平面,即C_∞=C∪{0},X表示复Banach空间,T表示X上的闭线性算于,D(T)表示T的定义域,σ(T),ρ(T)分别表示T的谱更多还原

【Abstract】 In this paper, having investegated some properties of closed spectral reducible operator on Banach space, we have obtained the necessary and sufficient condition for a closed operator becoming a closed spectral operator. The main results are as follows: (1) Let T be a closed spectral reducible operator, then for any closed subset F of complex plane, We have (2) Let T be a closed operator, then T becomes a closed spectral operator if and only if 1. T is a spectral reducible closed decomposable operator with property (B); 2. for every α∈ρ(T), the spectral measure E(·) of R(a,T) is satisfied with the condition E({0}) =0.更多还原