| B(X)上保持算子拟仿射性或值域稠性的线性映射 |
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| 引用本文： | 崔建莲,侯晋川.B(X)上保持算子拟仿射性或值域稠性的线性映射[J].数学年刊A辑(中文版),2003(1). |
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| 作者姓名： | 崔建莲 侯晋川 |
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| 作者单位： | 中国科学院数学与系统科学研究院 数学研究所(崔建莲)，山西师范大学数学与计算机系 北京(侯晋川) |
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| 基金项目： | 国家自然科学基金(No.10071046)，山西省自然科学基金(No.981009)资助的项目 |
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| 摘 要： | 设X和Y是无限维的复Banach空间,Φ是从B(X)到B(Y)保单位的线性满射.本文证明了Φ双边保算子的拟仿射性当且仅当Φ为同构或反同构;Φ双边保算子的值域稠性当且仅当Φ是同构.
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| 关 键 词： | 压缩谱 拟仿射 线性保持映射 |
LINEAR MAPS PRESERVING QUASI-AFFINITY OR RANGE DENSITY OF OPERATORS ON B(X) |
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| CUI Jianlian HOU JinchuanInstitute of Mathematics,Academy of Mathematics and System Sciences,Chinese Academy of Sciences,Beijing ,China.LINEAR MAPS PRESERVING QUASI-AFFINITY OR RANGE DENSITY OF OPERATORS ON B(X)[J].Chinese Annals of Mathematics,2003(1). |
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| Authors: | CUI Jianlian HOU JinchuanInstitute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China |
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| Institution: | CUI Jianlian HOU JinchuanInstitute of Mathematics,Academy of Mathematics and System Sciences,Chinese Academy of Sciences,Beijing 100080,China.Department of Mathematics,Shanxi Teachers University,Linfen 041004,Shanxi,China. E-mail: jhou@dns.sxtu.edu.cn |
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| Abstract: | Let X and Y be two infinite dimensional complex Banach spaces, and let be a unital linear surjection from B(X) onto B(Y). The authors prove that preserves the quasi-affinity of operators in both directions if and only if it is either an isomorphism or an anti-isomorphism; 4 preserves the range density of operators in both directions if and only if it is an isomorphism. |
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| Keywords: | Compression spectrum Quasi-affinity Linear preservers |
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