Abstract
In this manuscript, we explore the form of a non-linear bijective maps on factor von Neumann algebras \(\textsf{M}\) and \(\textsf{N}\) such that \(\varOmega :\textsf{M}\rightarrow \textsf{N}\) satisfies \(\varOmega (\texttt {m} ~\diamondsuit ~ \texttt {n})=\varOmega (\texttt {n})~\diamondsuit ~\varOmega (\texttt {m})\), where \(\texttt {m}~\diamondsuit ~ \texttt {n}=\texttt {m}^{*}{} \texttt {n}+\texttt {n}^{*}{} \texttt {m}\), for all \(\texttt {m},\texttt {n}\in \textsf{M}\).
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References
Bai, Z.F., Du, S.P.: Maps preserving products \(XY-YX^\ast \) on von Neumann algebras. J. Math. Anal. Appl. 386(1), 103–109 (2012)
Jodran mappings of semiprime rings: Bres̆ar, M. J. Algebra 127, 218–228 (1989)
Cui, J., Li, C.K.: Maps preserving product \(XY-Y X^\ast \) on factor von Neumann algebras. Linear Algebra Appl. 431(5–7), 833–842 (2009)
Dai, L., Lu, F.: Nonlinear maps preserving Jordan \(\ast -\)products. J. Math. Anal. Appl. 409(1), 180–188 (2014)
Huo, D., Zheng, B., Xu, J., Liu, H.: Nonlinear mappings preserving Jordan multiple \(\ast -\)product on factor von Neumann algebras. Linear Multilinear Algebra 63(5), 1026–1036 (2015)
Ji, P., Liu, Z.: Additivity of Jordan maps on standard Jordan operator algebras. Linear Algebra Appl. 430(1), 335–343 (2009)
Li, C., Lu, F., Fang, X.: Nonlinear mappings preserving product \(XY+YX^\ast \) on factor von Neumann algebras. Linear Algebra Appl. 438, 2339–2345 (2013)
Lu, F.: Additivity of Jordan maps on standard operator algebras. Linear Algebra Appl. 357, 123–131 (2002)
Lu, F.: Jordan triple maps. Linear Algebra Appl. 375, 311–317 (2003)
Lu, F.: Jordan maps on associative algebras. Comm. Algebra 31, 2273–2286 (2003)
Martindale, W.S., III.: When are multiplicative mappings additive? Proc. Amer. Math. Soc. 21, 695–698 (1969)
Taghavi, A., Darvish, V., Rohi, H.: Additivity of maps preserving products \(AP \pm PA^*\) on \(C^\ast -\)algebras. Math. Slov. 67, 213–220 (2017)
Taghavi, A., Razeghi, M.: Non-linear new product \(A^\ast B- B^\ast A\) derivation on \(\ast -\)algebra. Proyecciones (Antofagasta, On line) 39(2), 467–479 (2020)
Qi, X., Hou, J.: Additivity of Lie multiplicative maps on triangular algebras. Linear Multilinear Algebra 59, 391–397 (2011)
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The authors are grateful to the referees for their helpful feedback and suggestions.
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Arif Raza, M., Al-Sobhi, T. (2024). Non-linear Mappings Preserving Product \(\texttt {m}^{*}{} \texttt {n}+\texttt {n}^{*}{} \texttt {m}\) on Factor von Neumann Algebras. In: Ali, S., Ashraf, M., De Filippis, V., Rehman, N.u. (eds) Advances in Ring Theory and Applications. WARA 2022. Springer Proceedings in Mathematics & Statistics, vol 443. Springer, Cham. https://doi.org/10.1007/978-3-031-50795-3_24
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DOI: https://doi.org/10.1007/978-3-031-50795-3_24
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