Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (4): 978-988.

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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
  • Supported by:
    the NSFC(11601420);the Natural Science Basic Research Plan in Shaanxi Province(2018JM1053)


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

CLC Number: 

  • O177.1