Banach空间中闭线性算子广义预解式存在定理  

Existence Theorems for Generalized Resolvents of Closed Linear Operators in Banach Spaces

作　　者：黄强联[1] 马吉溥[2,3] 王丽[1] 

机构地区：[1]扬州大学数学科学学院,江苏扬州225002 [2]哈尔滨师范大学曾远荣泛函分析研究中心,哈尔滨150025 [3]南京大学数学系,南京210093

出　　处：《数学年刊（A辑）》2011年第5期635-646,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(10971182);江苏省自然科学基金(No.BK2009179;No.BK2010309);江苏省高校自然科学基金(No.07KJB110131;No.10KJB110012)资助的项目

摘　　要：在Banach空间中研究闭线性算子广义逆扰动问题和广义预解式存在性问题.给出了闭线性算子广义逆在T-有界扰动下的一些稳定特征,这些特征推广了在有界线性算子情形、闭线性算子有界扰动情形以及闭线性算子保值域或保核空间情形的一些已知结果.以此为基础,得到了闭线性算子广义预解式存在的一些充要条件及其广义预解式的显式表达式.作为应用,给出了闭Fredholm算子和闭半-Fredholm算子的广义预解式存在性特征.The perturbation problem for the generalized inverses and the existence for generalized resolvents of closed linear operators in Banach spaces are studied.The authors first provide some stability characterizations of generalized inverses of closed linear operator under T-bounded perturbation,which improves some well-known results in the case of bounded linear operators,of closed linear operators under bounded perturbation and of that the perturbation does not change the null space and the range of closed linear operators,respectively. Based on these results,some sufficient and necessary conditions for the existence of the generalized resolvents of closed linear operators are obtained.An explicit expression of the generalized resolvent is also given.As applications,the characterizations for the existence of generalized resolvents of closed Predholm operators and closed semi-Predholm operators are also obtained.

关 键 词：广义逆 广义预解式 闭线性算子 闭Fredholm算子 闭半-Fredholm算子 

分 类 号：O177.2[理学—数学]