| 对称算子空间上的保秩1线性映射 |
| |
| 引用本文： | 张国栋,刘绍武.对称算子空间上的保秩1线性映射[J].黑龙江大学自然科学学报,2006,23(2):235-238. |
| |
| 作者姓名： | 张国栋 刘绍武 |
| |
| 作者单位： | 黑龙江大学,数学科学学院,黑龙江,哈尔滨,150080 |
| |
| 基金项目： | Supported by the Nature Science Foundation of Heilongjiang Education Committee (10541176) |
| |
| 摘 要： | 设H是一个复Hilbert空间,S(H)为H上对称算子全体所成的集合,用Γ表示S(H)中秩1算子全体所成的集合.设L是S(H)上的映射,如果L(Γ)Γ,则称L是保秩1的.S(H)上保秩1的弱连续线性映射被刻画.
|
| 关 键 词： | Hilbert空间 秩1 线性映射 对称算子 |
| 文章编号： | 1001-7011(2006)02-0235-04 |
| 修稿时间： | 2005年5月24日 |
Rank one preserving linear maps on spaces of symmetric operators |
| |
| ZHANG Guo-dong,LIU Shao-wu.Rank one preserving linear maps on spaces of symmetric operators[J].Journal of Natural Science of Heilongjiang University,2006,23(2):235-238. |
| |
| Authors: | ZHANG Guo-dong LIU Shao-wu |
| |
| Abstract: | Let H be a complex Hilbert space, and let S(H) be the space of all symmetric operators on H. Denote by Γ the subset of S(H) consisting of all rank one operators. A linear map L from S(H)to itself is called a rank one preserver on S(H) if L(Γ) (∈) Γ. A complete classification of all linear and weakly continuous rank one preservers on S(H) is given. |
| |
| Keywords: | Hilbert space rank one linear map symmetric operator |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
