| 一秩元集上完全保反对合性的可加映射 |
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| 引用本文： | 刘敏,黄丽,李俊林.一秩元集上完全保反对合性的可加映射[J].太原科技大学学报,2012(1):62-65. |
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| 作者姓名： | 刘敏 黄丽 李俊林 |
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| 作者单位： | 太原科技大学应用科学学院 |
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| 基金项目： | 太原科技大学博士科研启动基金(20082024) |
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| 摘 要： | 主要刻画了一秩元集上完全保反对合性的可加映射,证明了这样的映射是同构的常数倍或(复情形下)共轭同构的常数倍。对于映射Φ∶R→,对于每个n∈瓔,定义映射Φn为Φn((sij)n×n)=(Φ(sij))n×n.则如果Φn保反对合性,称Φ是n-保反对合性的;如果对于每个正整数n,Φ是n-保反对性的,则称Φ是完全保反对合性的。
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| 关 键 词： | 一秩元集 完全保持问题 反对合性 可加映射 |
Additive Maps Completely Preserving Anti-involution on Set of Rank One Operators |
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| LIU Min,HUANG Li,LI Jun-lin.Additive Maps Completely Preserving Anti-involution on Set of Rank One Operators[J].Journal of Taiyuan University of Science and Technology,2012(1):62-65. |
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| Authors: | LIU Min HUANG Li LI Jun-lin |
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| Institution: | (School of Applied Sciences,Taiyuan University of Science and Technology,Taiyuan 030024,China) |
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| Abstract: | Additive maps between the sets of rank-one operators completely preserving anti-involution are characterized,and such maps are proved to be an constant times of isomorphisms or(in the complex case)conjugate isomorphisms.To map Φ∶ R→χ and each n ∈N,a map Φn is defined as Φn((sij)n×n)=(Φ(sij))n×n.If Φn preserves anti-involution,Φ is n-anti-involution preserving.And if Φ is n-anti-involution preserving for every positive integer n,Φ is completely anti-involution preserving. |
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| Keywords: | sets of rank one operators complete preserver problems anti-involution additive maps |
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