数学物理学报 ›› 2021, Vol. 41 ›› Issue (4): 978-988.

• 论文 • 上一篇    下一篇

因子von Neumann代数上的非线性$\xi$-Jordan *-三重可导映射

张芳娟1,*(),朱新宏2   

  1. 1 西安邮电大学理学院 西安 710121
    2 西安现代控制技术研究所 西安 710065
  • 收稿日期:2020-08-10 出版日期:2021-08-26 发布日期:2021-08-09
  • 通讯作者: 张芳娟 E-mail:zhfj888@xupt.edu.cn
  • 基金资助:
    国家自然科学基金(11601420);陕西省自然科学基础研究计划资助项目(2018JM1053)

Nonlinear $\xi$-Jordan *-Triple Derivable Mappings on Factor von Neumann Algebras

Fangjuan Zhang1,*(),Xinhong Zhu2   

  1. 1 School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121
    2 Xi'an Modern Control Technology Institute, Xi'an 710065
  • Received:2020-08-10 Online:2021-08-26 Published:2021-08-09
  • Contact: Fangjuan Zhang E-mail:zhfj888@xupt.edu.cn
  • Supported by:
    the NSFC(11601420);the Natural Science Basic Research Plan in Shaanxi Province(2018JM1053)

摘要:

${\cal A}$是因子von Neumann代数,$\xi$是非零复数.非线性映射$\phi:{\cal A\rightarrow A}$满足对所有$A,B,C\in{\cal A},$$\phi (A\diamond_{\xi}B\diamond_{\xi}C)=\phi (A)\diamond_{\xi}B\diamond_{\xi}C+A\diamond_{\xi}\phi (B)\diamond_{\xi}C+A\diamond_{\xi}B\diamond_{\xi}\phi (C)$当且仅当$\phi$是可加的*-导子且对所有$A\in{\cal A},$$\phi (\xi A)=\xi\phi (A).$

关键词: ξ-Jordan*-三重可导映射, von Neumann代数, *-导子

Abstract:

Let ${\cal A}$ be a factor von Neumann algebra and $\xi$ be a non-zero complex number. A nonlinear map $\phi:\mathcal A\rightarrow\mathcal A$ has been demonstrated to satisfy $\phi(A\diamond_{\xi}B\diamond_{\xi}C)=\phi(A)\diamond_{\xi}B\diamond_{\xi}C+A\diamond_{\xi}\phi(B)\diamond_{\xi}C+A\diamond_{\xi}B\diamond_{\xi}\phi(C)$ for all $A, B, C\in\mathcal A$ if and only if $\phi$ is an additive *-derivation and $\phi(\xi A)=\xi\phi(A)$ for all $A\in\mathcal A.$

Key words: ξ-Jordan *-triple derivable mapping, von Neumann algebra, *-Derivation

中图分类号: 

  • O177.1