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Nonlinear maps preserving bi-skew Jordan triple product on factor von Neumann algebras

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Abstract

Let \({\mathcal {A}}\) be a factor von Neumann algebra with dim\(({\mathcal {A}})\ge 2\). For any \(A, B\in {\mathcal {A}}\), a product \( A\mathbin {\triangle }B=A^{*}B+B^{*}A\) is called a bi-skew Jordan product. In this paper, it is proved that every bijective map preserving bi-skew Jordan triple product on \({\mathcal {A}}\) 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 are grateful to the anonymous referees and editors for their work.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People’s Republic of China

    Dongfang Zhang, Changjing Li & YuanYuan Zhao

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  1. Dongfang Zhang
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  2. Changjing Li
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  3. YuanYuan Zhao
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Correspondence to Changjing Li.

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The authors are 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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Zhang, D., Li, C. & Zhao, Y. Nonlinear maps preserving bi-skew Jordan triple product on factor von Neumann algebras. Period Math Hung 86, 578–586 (2023). https://doi.org/10.1007/s10998-022-00492-4

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