| 标准C*-代数间保持一类正元比较关系的映射 |
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| 引用本文： | 方小春,赵冬,徐小明.标准C*-代数间保持一类正元比较关系的映射[J].同济大学学报(自然科学版),2011,39(12):1880-1882. |
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| 作者姓名： | 方小春 赵冬 徐小明 |
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| 作者单位： | 1. 同济大学数学系,上海,200092
2. 同济大学数学系,上海 200092;上海应用技术学院理学院,上海 201418 |
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| 基金项目： | 国家自然科学基金项目（(10771161） |
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| 摘 要： | 假设H是一个复Hilbert空间,AH是H上的一个标准C*-代数,AH+是AH中所有正元构成的集合.1977年,Cuntz引入了C*-代数中正元的比较关系.设A是一个C*-代数,任给A,B∈A+,若存在X∈A+,使得A=XBX*,则记A≤B.文章刻画了定义在AH+上的所有双边保持此关系的弱连续半线性满射.
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| 关 键 词： | 标准C*-代数 比较关系 保持映射 |
| 收稿时间： | 2010/9/25 0:00:00 |
| 修稿时间： | 3/4/2011 8:11:07 PM |
Mapping on Standard C*algebras Preserving Comparison for Positive Elements |
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| FANG Xiaochun,ZHAO Dong and XU Xiaoming.Mapping on Standard C*algebras Preserving Comparison for Positive Elements[J].Journal of Tongji University(Natural Science),2011,39(12):1880-1882. |
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| Authors: | FANG Xiaochun ZHAO Dong and XU Xiaoming |
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| Institution: | Department of Mathematics,Tongji University,Shanghai 200092,China;Department of Mathematics,Tongji University,Shanghai 200092,China;Department of Mathematics,Tongji University,Shanghai 200092,China; Shanghai Insititule of Technology,School of Science,Shanghai 201418,China |
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| Abstract: | Let H be a complex Hilbert space,AH the standard C*-algebra on H,and AH+ the set of all positive elements in AH.In 1977,Cuntz introduced a comparison in the set of all positive elements in a C*-algebra.Let A be a C*-algebra.For A,B∈A+,we write A≤B if there exists an element X∈A such that A=XBX*.In this paper,we characterize all weakly continuous semilinear surjective maps on AH+ which preserves the positive elements comparison in both directions. |
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| Keywords: | standard C*-algebras comparison relation preserving mapping |
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