| Wigner定理在保持算子乘积范数正映射的应用 |
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| 引用本文： | 李晋秀.Wigner定理在保持算子乘积范数正映射的应用[J].数学研究,2004,37(1):11-16. |
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| 作者姓名： | 李晋秀 |
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| 作者单位： | 东华大学理学院应用数学系,上海,200051 |
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| 基金项目： | This research is supported by Shanghai Science and Technology Commission，grant(0 1 ZA1 4 0 0 3) |
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| 摘 要： | 把Wigner定理应用于算子代数上的保持映射问题,证明了如果φ是标准算子代数上的正映射,且保持两个算子乘积的范数或奇异值的和,则φ必定具有形式φ(A)=UAU*,其中U是一个酉算子或反酉算子.
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| 关 键 词： | Wigner定理 算子代数 保持问题 范数 奇异值 |
Applications of Wigner's Theorem to Positive Maps Preserving Norm of Operator Products |
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| Abstract.Applications of Wigner''''s Theorem to Positive Maps Preserving Norm of Operator Products[J].Journal of Mathematical Study,2004,37(1):11-16. |
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| Authors: | Abstract |
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| Abstract: | We apply Wigner's theorem to positive maps on standard operator algebras which preserve norm or sum of singular values of operator products. It follows that such maps are of the form φ(A)=UAU* with U either an unitary or antiunitary operator. |
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| Keywords: | Wigner's theorem preserver problem operator algebra norm singular value |
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