Nonlinear Maps Preserving Mixed Jordan Triple Products on von Neumann Algebras
Received:September 24, 2021  Revised:February 19, 2022
Key Word: mixed Jordan triple product   isomorphism   von Neumann algebras  
Fund ProjectL:Supported by the Natural Science Foundation of Shandong Province (Grant No.ZR2018BA003) and the National Natural Science Foundation of China (Grant No.11801333).
Author NameAffiliation
Dongfang ZHANG School of Mathematics and Statistics, Shandong Normal University, Shandong 250014, P. R. China 
Changjing LI School of Mathematics and Statistics, Shandong Normal University, Shandong 250014, P. R. China 
Yuanyuan ZHAO School of Mathematics and Statistics, Shandong Normal University, Shandong 250014, P. R. China 
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Abstract:
      In this paper, we prove that if a bijective map $\Phi$ preserves mixed Jordan triple products between von Neumann algebras with no central abelian projections, then $\Phi(I)\Phi$ is the sum of a linear $*$-isomorphism and a conjugate linear $*$-isomorphism, where $\Phi(I)$ is a self-adjoint central element in the range with $\Phi(I)^{2}=I$. Also, we give the structure of this map that preserves mixed Jordan triple products between factor von Neumann algebras.
Citation:
DOI:10.3770/j.issn:2095-2651.2022.04.004
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