Nonlinear Maps Preserving the Mixed Triple Products between Factors
Received:March 18, 2021  Revised:October 16, 2021
Key Word: mixed triple product   isomorphism   factor
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11601420), the Natural Science Foundation of Shaanxi Province (Grant No.2018JM1053) and the Natural Science Basic Research Plan in Shaanxi Province (Grant No.16JK1686).
 Author Name Affiliation Fangjuan ZHANG School of Science, Xi'an University of Posts and Telecommunications, Shaanxi 710121, P. R. China Xinhong ZHU Xi'an Modern Control Technology Institute, Shaanxi 710065, P. R. China
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Let $\mathcal{A}$ and $\mathcal{B}$ be two factors with $\dim\mathcal{A}>4$. In this paper, it is proved that a bijective map $\phi:\mathcal{A}\rightarrow\mathcal{B}$ satisfies $\phi([A,B]\bullet C)=[\phi(A),\phi(B)]\bullet\phi(C)$ for all $A,B,C\in\mathcal A$ if and only if $\phi$ is a linear $*$-isomorphism, or a conjugate linear $*$-isomorphism, or the negative of a linear $*$-isomorphism, or the negative of a conjugate linear $*$-isomorphism.