Zhujun Yang, Jianhua Zhang. Source: Annals of Functional Analysis, Volume 10, Number 3, 325--336.Abstract:
We prove that every bijective map that preserves mixed Lie triple products from a factor von Neumann algebra $\mathcal{M}$ with $\dim \mathcal{M}\gt 4$ into another factor von Neumann algebra $\mathcal{N}$ is of the form $A\rightarrow \epsilon \Psi (A)$ , where $\epsilon \in \{1,-1\}$ and $\Psi :\mathcal{M}\rightarrow \mathcal{N}$ is a linear $*$ -isomorphism or a conjugate linear $*$ -isomorphism. Also, we give the structure of this map when $\dim \mathcal{M}=4$ .