Annals of Functional Analysis

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

Zhujun Yang and Jianhua Zhang

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We prove that every bijective map that preserves mixed Lie triple products from a factor von Neumann algebra M with dimM>4 into another factor von Neumann algebra N is of the form AϵΨ(A), where ϵ{1,1} and Ψ:MN is a linear -isomorphism or a conjugate linear -isomorphism. Also, we give the structure of this map when dimM=4.

Article information

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

Received: 17 July 2018
Accepted: 6 November 2018
First available in Project Euclid: 6 August 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B49: Transformers, preservers (operators on spaces of operators)
Secondary: 46B10: Duality and reflexivity [See also 46A25]

preserver mixed Lie triple product von Neumann algebra


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.

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