| 自伴算子空间上保持Jordan积范数的映射 |
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| 引用本文： | 石欢欢,吉国兴.自伴算子空间上保持Jordan积范数的映射[J].山东大学学报(理学版),2010,45(3):80-84. |
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| 作者姓名： | 石欢欢 吉国兴 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,陕西西安,710062 |
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| 摘 要： | 设H是复数域C上的Hilbert空间且dimH≥2,Bs(H)是H上所有自伴算子全体。设Φ是Bs(H)上的双射,如果Φ满足对任意A,B∈Bs(H),都有‖Φ(A)Φ(B)+Φ(B)Φ(A)‖=‖AB+BA‖,则存在一个酉算子或反酉算子U和泛函h:B(H)→{1,-1}使得对任意X∈B(H),有Φ(X)=h(X)UXU*。
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| 关 键 词： | 自伴算子 Jordan积 范数 |
| 收稿时间： | 2009-05-19 |
Maps preserving norms of Jordan products on the space of self-adjoint operators |
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| SHI Huan-huan,JI Guo-xing.Maps preserving norms of Jordan products on the space of self-adjoint operators[J].Journal of Shandong University,2010,45(3):80-84. |
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| Authors: | SHI Huan-huan JI Guo-xing |
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| Institution: | College of Mathematics and Information Science, Xi’an 710062, Shaanxi, China |
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| Abstract: | Abstract: Let H be a complex Hilbert space with dimH≥2 and let B_s,(H) be the space of all self-adjoint operators on H. Let Ф be a bijective map on B_s, (H) . It is proved that if ‖Ф(A)Ф(B)+Ф(B)Ф(A)‖= ‖AB+BA‖for all A,B ∈ B_s, (H), then there is a unitary operator or a conjugate unitary operator U and a functional h from B_s, (H) to {1, -1} such that Ф(X) = h(X) UXU~* for all X ∈ B_s, (H). |
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| Keywords: | self-adjoint operator Jordan product norm |
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