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

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

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 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 Zhang^1,*(),Xinhong Zhu²

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/Abstract

摘要：

设 ${\cal A}$ 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 $A，B，C\in{\cal A}，$ 有 $\phi （A\diamond_{\xi}B\diamond_{\xi}C）=\phi （A）\diamond_{\xi}B\diamond_{\xi}C+A\diamond_{\xi}\phi （B）\diamond_{\xi}C+A\diamond_{\xi}B\diamond_{\xi}\phi （C）$ 当且仅当 $\phi$ 是可加的*-导子且对所有 $A\in{\cal A}，$ 有 $\phi （\xi A）=\xi\phi （A）.$

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

张芳娟,朱新宏. 因子von Neumann代数上的非线性 $\xi$ -Jordan *-三重可导映射[J]. 数学物理学报, 2021, 41(4): 978-988.

Fangjuan Zhang,Xinhong Zhu. Nonlinear $\xi$ -Jordan *-Triple Derivable Mappings on Factor von Neumann Algebras[J]. Acta mathematica scientia,Series A, 2021, 41(4): 978-988.

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