Non-linear Mappings Preserving Product \(\texttt {m}^{*}{} \texttt {n}+\texttt {n}^{*}{} \texttt {m}\) on Factor von Neumann Algebras
摘要
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 \(\texttt {m},\texttt {n}\in \textsf{M}\) .