| Nonlinear Maps Preserving the Mixed Triple Products between Factors |
| Received:March 18, 2021 Revised:October 16, 2021 |
| Key Words:
mixed triple product isomorphism factor
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| Fund Project: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). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2022.03.008 |
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