| B(H)上的保拟相似线性映射 |
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| 引用本文： | 王琳琳,张芳娟,吉国兴,庞永锋.B(H)上的保拟相似线性映射[J].西安建筑科技大学学报(自然科学版),2007,39(3):440-443. |
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| 作者姓名： | 王琳琳 张芳娟 吉国兴 庞永锋 |
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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. 陕西师范大学数学与信息科学学院,陕西,西安,710062;西安建筑科技大学理学院,陕西,西安,710055 |
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| 摘 要： | 研究了B(H)上的拟相似不变子空间和保拟相似线性映射,其中H是复可分的无限维Hilbert空间,B(H)是由H上的有界线性算子全体所组成的Banach代数.由于拟相似不变子空间一定是相似不变子空间,因此由已知定理可得出B(H)上的拟相似不变子空间共有三种形式,即{0},CI和B(H).应用线性算子逼近的方法,证明了B(H)上的每一个有界满的保拟相性映射一定是零乘以一个自同构或反自同构.
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| 关 键 词： | 线线算子 相似 拟相 拟相 性映射 |
| 文章编号： | 1006-7930（2007）03-0440-04 |
| 修稿时间： | 2005-05-20 |
Quasisimialarity-preserving linear maps on B(H) |
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| WANG LIN-lin,ZHANG Fang-juan,JI Guo-xing,PANG Yong-feng.Quasisimialarity-preserving linear maps on B(H)[J].Journal of Xi'an University of Architecture & Technology,2007,39(3):440-443. |
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| Authors: | WANG LIN-lin ZHANG Fang-juan JI Guo-xing PANG Yong-feng |
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| Abstract: | As H is let to be a separable infinite dimensional Hilbert space and B(H) the Banach algebra of all bounded linear operators on H,the quasisimilarity-invariant subspaces of B(H) and quasisimilarity-preserving linear maps on B(H) is put to study.The study of this paper proved that the quasisimilarity-invariant subspaces of B(H) have three forms,that is {0},CI and B(H) and that every bounded linear surjective map on B(H) which is quasisimilarity-preserving is nonzero scalar multiple of either an automorphism or an anti-automorphism by using the method of linear operator approximation. |
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| Keywords: | linearoperator similarity quasisimilarity quasisimilarity-preserving linear map |
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