| Von Neumann代数上的广义Jordan可导映射 |
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| 引用本文： | 张存侠. Von Neumann代数上的广义Jordan可导映射[J]. 西北纺织工学院学报, 2008, 0(5): 639-641 |
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| 作者姓名： | 张存侠 |
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| 作者单位： | [1]陕西师范大学数学与信息科学学院,陕西西安710062; [2]陕西教育学院数理工程系,陕西西安710061 |
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| 基金项目： | 国家自然科学基金资助项目（10571114） |
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| 摘 要： | 设φ：A一A是一个线性映射，如果任意A，B∈A且AB＋BA=I，有φ（AB＋BA）=φ（A）B＋Aφ（B）＋Bφ（A）＋φ（B）A—Aφ（I）B-Bφ（I）A，则称φ是A上的单位广义Jordan可导映射；如果任意A，B∈A且AB＋BA=0，有φ（AB＋BA）=φ（A）B＋Aφ（B）＋Bφ（A）＋φ（B）A-Aφ（I）B-Bφ（I）A，则称φ是A上的零点广义Jordan可导映射．证明了Von Neumann代数上的每个范数拓扑连续的单位广义Jordan可导映射与零点广义Jordan可导映射都是广义内导子．
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| 关 键 词： | 广义Jordan可导映射 广义导子 Von Neumann代数 |
Generalized Jordan derivable mappings on Von Neumann algebras |
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| ZHANG Cun-xia. Generalized Jordan derivable mappings on Von Neumann algebras[J]. Journal of Northwest Institute of Textile Science and Technology, 2008, 0(5): 639-641 |
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| Authors: | ZHANG Cun-xia |
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| Affiliation: | ZHANG Cun-xia (1. College of Mathematics and Information Science, Shaanxi Normal University, Xi＇ an 710062, China; 2. Department of Maths, Physics and Engineering, Shaanxi Institute of Education, Xi＇an 710061, China) |
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| Abstract: | If A is a Von Neumann algebras, φ is a linear map from A to A. If arbitary A, B ∈ and AB＋BA= I,then φ（AB＋BA）=φ（A）B＋Aφ（B）＋φ（B）A＋Bφ（A）-Aφ（I）B-Bφ（I）A, it is said that φ is a generalized Jordan derivable mapping at unit operator. If arbitary A,B∈ A and AB＋BA=0,then φ（AB＋BA）=φ（A）B＋Aφ（B）＋φ（B）A＋Bφ（A）-A＋（I）B-Bφ（I）A,it is said that φ is a generalized Jordan derivable mapping at zero operator. In this paper,it is proved that every norm continuous generalized Jordan derivable mapping at wnit operator or generalized Jordan derivable mapping at zero operator on any Von Neumann algebra is a generalized inner derivation. |
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| Keywords: | generalized Jordan derivable mapping generalized dereivation Von Neumann algebra |
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