Annals of Functional Analysis

Nonlinear maps preserving the Jordan triple -product on von Neumann algebras

Changjing Li, Fangyan Lu, and Ting Wang

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This article investigates a bijective map Φ between two von Neumann algebras, one of which has no central abelian projections, satisfying Φ([[A,B],C])=[[Φ(A),Φ(B)],Φ(C)] for all A,B,C in the domain, where [A,B]=ABBA* is the skew Lie product of A and B. We show that the map Φ(I)Φ is a sum of a linear -isomorphism and a conjugate linear -isomorphism, where Φ(I) is a self-adjoint central element in the range with Φ(I)2=I.

Article information

Ann. Funct. Anal., Volume 7, Number 3 (2016), 496-507.

Received: 30 October 2015
Accepted: 11 February 2016
First available in Project Euclid: 22 August 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B48: Operators on Banach algebras
Secondary: 46L10: General theory of von Neumann algebras

Jordan triple $*$-product isomorphism von Neumann algebras


Li, Changjing; Lu, Fangyan; Wang, Ting. Nonlinear maps preserving the Jordan triple $*$ -product on von Neumann algebras. Ann. Funct. Anal. 7 (2016), no. 3, 496--507. doi:10.1215/20088752-3624940.

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