保持斜ξ-Lie零积的可加映射

齐霄霏 已出版文章查询
齐霄霏
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1 侯晋川 已出版文章查询
侯晋川
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jinchuanhou@aliyun.com
2 * 崔建莲 已出版文章查询
崔建莲
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1山西大学数学科学学院 太原030006

2太原理工大学数学学院 太原030024

3清华大学数学科学系 北京100084


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HK是维数大于2的复Hilbert空间, ξ∈C. 假设Φ:B(H)→B(K)是满足对任意A,BB(H) 都有AB=ξBA* ⇔ Φ(A)Φ(B)=ξΦ(B)Φ(A)* 的可加满射. 本文证明了, (1) 如果ξ=1,则存在酉或反酉算子U:H→K以及非零实数c使得Φ(A)=cUAU* 对所有AB(H) 成立; (2) 如果ξ∈R\{1} 且Φ 保单位元, 则存在酉或反酉算子U:H→K使得Φ(A)=UAU* 对所有A,BB(H)成立; (3) 如果ξ∈C\R且Φ 保单位元, 则存在酉算U:H→K使得Φ(A)=UAU*对所有A,BB(H)成立.

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DOI: http://dx.doi.org/10.1360/012014-69

语种: 中文   

基金国家自然科学基金(批准号: 11171249, 11101250 和11271217);山西省青年研究基金(批准号:...

关键词Hilebert 空间上的算子 可加映射 斜Lie 积 *-同构


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