| Banach空间中线性算子的(集值)度量广义逆及其齐性单值选择 |
| |
| 引用本文： | 王玉文,潘少荣.Banach空间中线性算子的(集值)度量广义逆及其齐性单值选择[J].数学学报,2003,46(3):431-438. |
| |
| 作者姓名： | 王玉文 潘少荣 |
| |
| 作者单位： | 哈尔滨师范大学数学,系哈尔滨,150080 |
| |
| 基金项目： | 国家自然科学基金(19971023)，黑龙江省自然科学基金资助项目 |
| |
| 摘 要： | 为研究Banach空间中不适定线性算子方程的最佳逼近解,Nashed在文1]中引入了Banach空问中线性算子T的(集值)度量广义逆T的概念,并提出“求解线性算子的(集值)度量广义逆的具有良好性质的单值选择是值得研究”的公开问题.本文首先证明了Banach空间中线性算子的度量广义逆是具有闭凸值的集值映射,给出了该度量广义逆的等价表达式,并利用Banach空间的再赋范方法,给出其有界齐性的单值选择,部分地解决了Nashed所提出的公开问题.
|
| 关 键 词： | Banach空间 对偶映射 度量投影 有界齐性算子 度量广义逆 |
| 文章编号： | 0583-1431(2003)03-0431-08 |
| 修稿时间： | 2001年12月13 |
The Set-Valued Metric Generalized Inverse of Linear Operator in Banach Space and Its Bounded Homogeneous Single Selection |
| |
| Yu Wen WANG Shao Rong PAN.The Set-Valued Metric Generalized Inverse of Linear Operator in Banach Space and Its Bounded Homogeneous Single Selection[J].Acta Mathematica Sinica,2003,46(3):431-438. |
| |
| Authors: | Yu Wen WANG Shao Rong PAN |
| |
| Institution: | Yu Wen WANG Shao Rong PAN (Department of Mathematics, Harbin Normal University, Harbin 150080, P. R. China) |
| |
| Abstract: | In this paper, the representation of the set-valued metric generalized inverse of closed linear operator with closed range in reflexive Banach space and its single selection are given. By the geometric property of the space, we prove that single selection of set-valued metric generalized inverse is a bounded homogeneous operator. |
| |
| Keywords: | Banach space Dual mapping Metric projection Bounded homogeneous operator Metric generalized inverse |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
| 点击此处可从《数学学报》浏览原始摘要信息 |
| 点击此处可从《数学学报》下载免费的PDF全文 |
