| 保持谱半径的乘法映射 |
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| 引用本文： | 赵玉松,唐瑞娜.保持谱半径的乘法映射[J].应用泛函分析学报,2001,3(3):231-235. |
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| 作者姓名： | 赵玉松 唐瑞娜 |
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| 作者单位： | 烟台师范学院数学系烟台 264025 |
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| 摘 要： | 设X和Y为无限维Banach空间，Φ：B（X）→B（Y）是保持谱半径的满射，且秩为1算子，则Φ具有形式Φ（T）=ATA∧-1，这里A：X→Y或是线性拓扑同构映射或是线性拓扑同构映射的共轭。
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| 关 键 词： | 谱半径 乘法映射 秩1算子 Eanach空间 同构映射 |
Multiplicative Maps Preserving the Spectral Radius |
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| ZHAO Yu-song,TANG Rui-na.Multiplicative Maps Preserving the Spectral Radius[J].Acta Analysis Functionalis Applicata,2001,3(3):231-235. |
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| Authors: | ZHAO Yu-song TANG Rui-na |
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| Institution: | ZHAO Yu-song,TANG Rui-na Department of Mathematics,Yantai Teachers College,Yantai Shandong 264025,China |
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| Abstract: | Let X and Y be infinite-dimensional Banach spaces. If φ: B(X) → B(Y) is a surjective
multiplicative map preserving the spectral radius of rank one operators, then φ is of the form φ (T) =
ATA-1. Where A: X → Y is either a linear topological isomorphism or a conjugate linear topological
isomorphism. |
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| Keywords: | spectral radius multiplicative map rank one operator |
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