Abstract
Let \({\mathcal {A}}\) and \({\mathcal {B}}\) be two factors with dim\({\mathcal {A}}>4\). In this article, it is proved that a bijective map \(\Phi : {\mathcal {A}}\rightarrow {\mathcal {B}}\) satisfies \(\Phi ([A\bullet B, C])=[\Phi (A)\bullet \Phi (B), \Phi (C)]\) for all \(A, B, C\in {\mathcal {A}}\) if and only if \(\Phi \) 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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Acknowledgements
The authors would like to thank the referee for the very thorough reading of the paper and many helpful comments. The second author is supported by the Natural Science Foundation of Shandong Province, China (Grant No. ZR2018BA003) and the National Natural Science Foundation of China (Grant No. 11801333).
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Communicated by Shirin Hejazian.
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Zhao, Y., Li, C. & Chen, Q. Nonlinear Maps Preserving Mixed Product on Factors. Bull. Iran. Math. Soc. 47, 1325–1335 (2021). https://doi.org/10.1007/s41980-020-00444-z
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DOI: https://doi.org/10.1007/s41980-020-00444-z