| 保持算子乘积投影的线性映射 |
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| 引用本文： | 吉国兴,曲凡连.保持算子乘积投影的线性映射[J].数学学报,2010,53(2):315-322. |
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| 作者姓名： | 吉国兴 曲凡连 |
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| 作者单位： | 陕西师范大学数学与信息科学学院; |
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| 基金项目： | 国家自然科学基金资助项目(10971123) |
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| 摘 要： | 设B(H)是复Hilbert空间H上的有界线性算子全体且dim H≥2.本文证明了B(H)上的线性满射φ保持两个算子乘积非零投影性的充分必要条件是存在B(H)中的酉算子U以及复常数λ满足λ~2=1,使得φ(X)=λU~*XU,(?)X∈B(H).同时也得到了线性映射保持两个算子Jordan三乘积非零投影的充分必要条件.
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| 关 键 词： | 线性映射 投影 算子乘积 |
| 收稿时间： | 2008-09-09 |
| 修稿时间： | 2009-09-24 |
Linear Maps Preserving Projections of Products of Operators |
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| Guo Xing JI Fan Lian QU College of Mathematics , Information Science,Shaanxi Normal University,Xi\'an ,P.R.China.Linear Maps Preserving Projections of Products of Operators[J].Acta Mathematica Sinica,2010,53(2):315-322. |
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| Authors: | Guo Xing JI Fan Lian QU College of Mathematics Information Science Shaanxi Normal University Xi\'an PRChina |
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| Institution: | College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, P. R. China |
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| Abstract: | Let B(H) be the algebra of all bounded linear operators on a complex Hilbert space H with dim H(?) 2.It is proved that a linear surjective map(?) on B(H) preserves the nonzero projections of products of two operators if and only if there is a unitary operator U in B(H) such that(?)(X)=λU~*XU,(?)X∈B(H) for some constantsλwithλ~2 = 1.Related results for linear surjective maps preserving Jordan triple products of two operators are also obtained. |
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| Keywords: | linear maps projections products of operators |
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