| 摘要: |
| 本文研究了套子代数上由零积确定的子集中保Jordan积的线性映射与同构和反同构的关系.证明了若对任意的A, B ∈ algMβ且AB=0,有φ(A ◦ B)=φ(A) ◦ φ(B)成立,则φ是同构或反同构.其中, algMβ, algMγ是因子von Neumann代数M中的两个非平凡套子代数,φ:algMβ → algMγ是一个保单位线性双射. |
| 关键词: 套子代数 Jordan 积 同构 |
| DOI： |
| 分类号:O177.1 |
| 基金项目:陕西省教育厅基金资助(12JK0875);西安科技大学培育基金资助(200845). |
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| CHARACTERIZATIONS OF JORDAN ISOMORPHISM ON NEST SUBALGEBRAS OF FACTOR VON NEUMANN ALGEBRAS |
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YANG Ai-li1, ZHANG Jian-hua2
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1.College of Sci., Xi'an University of Science and Technology, Xi'an 710054, China;2.College of Math. and Inform. Sci., Shaanxi Normal University, Xi'an 710062, China
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| Abstract: |
| This paper studied the relation between linear mappings preserving Jordan product in subset determined by zero product on nest subalgebras and isomorphism and anti isomorphism, and proved that if φ satisfies φ(A ◦ B)=φ(A) ◦ φ(B) for all A, B ∈ algMβ with AB=0, then φ is an isomorphism or an anti-isomorphism, where algMβ and algMγ be non-trivial nest subalgebras in the factor von Neumann algebra M, φ is a unital bijection. |
| Key words: nest subalgebra Jordan isomorphism isomorphism |
