## Annals of Functional Analysis

### Nonlinear maps preserving mixed Lie triple products on factor von Neumann algebras

#### 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 $\dim \mathcal{M}=4$.

#### Article information

Source
Ann. Funct. Anal., Volume 10, Number 3 (2019), 325-336.

Dates
Accepted: 6 November 2018
First available in Project Euclid: 6 August 2019

https://projecteuclid.org/euclid.afa/1565078418

Digital Object Identifier
doi:10.1215/20088752-2018-0032

Mathematical Reviews number (MathSciNet)
MR3989178

Zentralblatt MATH identifier
07089120

#### Citation

Yang, Zhujun; Zhang, Jianhua. Nonlinear maps preserving mixed Lie triple products on factor von Neumann algebras. Ann. Funct. Anal. 10 (2019), no. 3, 325--336. doi:10.1215/20088752-2018-0032. https://projecteuclid.org/euclid.afa/1565078418

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