Abstract
Let \(\mathcal{A}\) and \(\mathcal{B}\) be two factor von Neumann algebras. For \(A,B \in \mathcal{A}\), define by [A,B]* = AB − BA* the skew Lie product of A and B. In this article, it is proved that a bijective map \(\Phi :\mathcal{A} \to \mathcal{B}\) satisfies Φ([[A,B]*,C]*) = [[Φ(A),Φ(B)]*,Φ(C)]* for all \(A,B,C \in \mathcal{A}\) if and only if Φ is a linear *-isomorphism, or a conjugate linear *- isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.
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The authors would like to thank the referee for his valuable comments and suggestions.
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The work was supported by the National Natural Science Foundation of China (No. 11526123, No. 11401273) and the Natural Science Foundation of Shandong Province of China (No. ZR2015PA010).
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Li, C., Chen, Q. & Wang, T. Nonlinear Maps Preserving the Jordan Triple *-Product on Factor von Neumann Algebras. Chin. Ann. Math. Ser. B 39, 633–642 (2018). https://doi.org/10.1007/s11401-018-0086-4
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DOI: https://doi.org/10.1007/s11401-018-0086-4