| 黄强联,马吉溥,王丽.Banach空间中闭线性算子广义预解式存在定理[J].数学年刊A辑,2011,32(5):635~646 |
| 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 |
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| DOI： |
| 中文关键词: 广义逆 广义预解式 闭线性算子 闭Fredholm算子 闭半-Fredholm算子 |
| 英文关键词:Generalized inverse Generalized resolvent Closed linear operator Closed Fredholm operator Closed semi-Fredholm operator |
| 基金项目: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 |
| Author Name | Affiliation | E-mail | | HUANG Qianglian | College of Mathematics Science,Yangzhou University,Yangzhou 225002,Jiangsu,China. | qlhmath@ yahoo.com.cn | | MA Jipu | Yuan-Yung Tseng Functional Analysis Research Center,Harbin Normal University,Harbin 150025,China,Department of Mathematics,Nanjing | jipuma@126.com | | WANG Li | College of Mathematics Science,Yangzhou University,Yangzhou 225002,Jiangsu,China. | wangli-0911@163.com |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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 Fredholm
operators and closed semi-Fredholm operators are also obtained. |
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