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K(H)上保持*偏序的线性映射

Linear maps of preserving star partial order on K(H)
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摘要 设H表示无限维复可分Hilbert空间,K(H)表示H上所有紧算子的全体.研究了K(H)上保持*偏序的线性映射,若φ是K(H)上保持*偏序的线性双射,则存在非0常数α及H上的酉算子U和V,使得φ(X)=αUXV,X∈K(H);或反酉算子U和V,使得φ(X)=αUX*V,X∈K(H). Let ￡be a seperable infinite-dimensional complex Hilbert space and let ￡（￡） be the set of all compact operators on . Linear bijections on ￡（￡） preserving the star partial order was studied. It is proved that if is a linear bijection map on￡（￡） preserving the star partial order, then there exist a nonzero a E C, two unitary or anti-unitary operators U and V on such that （X）=aUXV for all X E Y（ （gD or （X）=aUX＊ V for all X∈￡（￡）
作者 张倩 吉国兴
机构地区 陕西师范大学数学与信息科学学院
出处 《纺织高校基础科学学报》 CAS 2013年第2期198-202,共5页 Basic Sciences Journal of Textile Universities
基金 国家自然科学基金资助项目(10971123)
关键词 偏序 酉算子 保持线性映射 star partial order unitary operator preserving linear map
分类号 O177.1 [理学—基础数学]
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参考文献12

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二级参考文献17

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纺织高校基础科学学报
2013年 第2期

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