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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (2): 41-47.doi: 10.6040/j.issn.1671-9352.0.2020.347

• • 上一篇    

von Neumann代数上保持混合Jordan三重η-积的非线性映射

庞永锋,张丹莉,马栋   

  1. 西安建筑科技大学理学院, 陕西 西安 710055
  • 发布日期:2021-01-21
  • 作者简介:庞永锋(1975— ),男,博士,教授,研究方向为算子理论与算子代数. E-mail:pangyongfengyw@xauat.edu.cn
  • 基金资助:
    陕西省自然科学基金资助项目(2019JM252)

Nonlinear maps preserving mixed Jordan triple η-product on the von Neumann algebras

PANG Yong-feng, ZHANG Dan-li, MA Dong   

  1. School of Science, Xian University of Architecture and Technology, Xian 710055, Shaanxi, China
  • Published:2021-01-21

摘要: 设M和N是2个维数大于1的因子von Neumann代数,任意一个保持混合Jordan三重η-(η≠-1)积的双射Φ:M→N有A→εΦ(A)的形式,其中ε∈{-1,1}。当η∈R时,εΦ是一个线性*-同构或者共轭线性*-同构;当η∈C\R时,εΦ是一个线性*-同构。

关键词: 因子von Neumann代数, 混合Jordan三重η-积, 同构

Abstract: Let M and N be two factor von Neumann algebras that their dimensions are larger than 1. It is proved that every bijective map preserving mixed Jordan triple η-products with η≠-1 from M into N is of the form A→εΦ(A), where ε∈{-1,1} and εΦ is a linear *-isomorphism or conjugate linear *-isomorphism when η∈R and εΦ is a linear *-isomorphism when η∈C\R.

Key words: factor von Neumann algebra, mixed Jordan triple η-product, isomorphism

中图分类号: 

  • O177.1
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