The Reducibility of Closed Operators on Banach Space

作     者：侯学章 Hou Xuezhang (Northeast Normal University)

作者机构：东北师范大学数学系 

出 版 物：《Chinese Quarterly Journal of Mathematics》 (数学季刊（英文版）)

年 卷 期：1989年第4卷第2期

页      面：49-55页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：闭算子 Banach空间 可分解算子 谱算子 扩充复平面 闭线性算子 解析扩张 类算子 充分必要条件 解析函数 

摘      要：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.