| 自伴算子空间上保因子乘积数值域的映射 |
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| 引用本文： | 贺衎,侯晋川,Dolinar GREGOR,Kuzma BONJA.自伴算子空间上保因子乘积数值域的映射[J].数学学报,2011(6). |
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| 作者姓名： | 贺衎 侯晋川 Dolinar GREGOR Kuzma BONJA |
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| 作者单位： | 太原理工大学数学系;Faculty of Electrical Engineering;University of Ljubljana;Trzaska 25;1000 Ljubljana;Slovenia;Institute of Mathematics;Physics;and Mechanics;Jadranska 19; |
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| 基金项目： | 国家自然科学基金资助项目(10771157) |
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| 摘 要： | 设H为复Hilbert空间,y_a(H)代表H上的有界自伴算子组成的空间,Φ:y_a(H)→y_a(H)是满射且复数ξ,n∈C\{1},则Φ满足W(AB-ξBA)=W(Φ(A)Φ(B)-ηΦ(B)Φ(A))对所有A,B∈y_a(H)成立当且仅当存在酉算子或者共轭酉算子U,使得Φ(A)=UAU*对所有A∈y_a(H)成立,或者Φ(A)=-UAU*对所有A∈y_a(H)成立.
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| 关 键 词： | 数值域 保持映射 因子乘积 |
Maps on Self-Adjoint Operators Preserving Numerical Range of Products up to a Factor |
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| Kan HE Jin Chuan HOU.Maps on Self-Adjoint Operators Preserving Numerical Range of Products up to a Factor[J].Acta Mathematica Sinica,2011(6). |
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| Authors: | Kan HE Jin Chuan HOU |
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| Institution: | Kan HE Jin Chuan HOU Department of Mathematics,Taiyuan University of Technology,Taiyuan 030024,P.R.China Dolinar GREGOR Faculty of Electrical Engineering,University of Ljubljana,Trzaska 25,1000 Ljubljana,Slovenia Kuzma BONJA Institute of Mathematics,Physics,and Mechanics,Jadranska 19,Slovenia |
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| Abstract: | Let H be a complex Hilbert space andy_a(H) the space of all self adjointoperators on H.Φ:y_a(H)→y_aa(H) is a surjectivc map.Forξ,μ∈C \ {1},thenΦsatisfies thatW(AB -ξBA) = W(Φ(A)Φ(B) -ηΦ(B)Φ(A))for all A,B∈y_a(H) if and only if there exists a unitary operator or con-unitaryoperator U such thatΦ(A) = UAU~* for all A∈y_a(H) orΦ(A) = -UAU~* for allA∈y_a(H). |
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| Keywords: | Numerical range preservers product up to a factor |
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