| Banach空间中闭线性算子广义预解式存在定理 |
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| 引用本文： | 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(中文版), 2011, 32(5): 635-646 |
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| 作者姓名： | 黄强联 马吉溥 王丽 |
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| 作者单位： | 扬州大学数学科学学院;哈尔滨师范大学曾远荣泛函分析研究中心;南京大学数学系; |
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| 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 |
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| 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.
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| 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 |
Existence Theorems for Generalized Resolvents of Closed Linear Operators in Banach Spaces |
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| HUANG Qianglian,MA Jipu and WANG Li. Existence Theorems for Generalized Resolvents of Closed Linear Operators in Banach Spaces[J]. Chinese Annals of Mathematics, 2011, 32(5): 635-646 |
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| Authors: | HUANG Qianglian MA Jipu WANG Li |
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| Affiliation: | HUANG Qianglian~1 MA Jipu~2 WANG Li~1 1 College of Mathematics Science,Yangzhou University,Yangzhou 225002,Jiangsu,China. 2 Yuan-Yung Tseng Functional Analysis Research Center,Harbin Normal University,Harbin 150025,China,Department of Mathematics,Nanjing University,Nanjing 210093,China. |
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| Abstract: | 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 li... |
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| Keywords: | Generalized inverse Generalized resolvent Closed linear operator Closed Fredholm operator Closed semi-Fredholm operator |
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