Let \(\mathcal {A}\) and \(\mathcal {B}\) be two factor von Neumann algebras. In this paper, we proved that a bijective mapping \(\varPhi :\mathcal {A}\rightarrow \mathcal {B}\) satisfies \(\varPhi (a\circ b-ba^{*})=\varPhi (a)\circ \varPhi (b)-\varPhi (b)\varPhi (a)^{*}\) (where \(\circ \) is the special Jordan product on \(\mathcal {A}\) and \(\mathcal {B},\) respectively), for all elements \(a,b\in \mathcal {A}\), if and only if \(\varPhi \) is a \(*\)-ring isomorphism. In particular, if the von Neumann algebras \(\mathcal {A}\) and \(\mathcal {B}\) are type I factors, then \(\varPhi \) is a unitary isomorphism or a conjugate unitary isomorphism.

令\（\ mathcal {A} \）和\（\ mathcal {B} \）为两个因子冯·诺依曼代数。在本文中，我们证明了双射映射\（\ varPhi：\ mathcal {A} \ rightarrow \ mathcal {B} \）满足\（\ varPhi（a \ circ b-ba ^ {*}）= \ varPhi（一个）\ CIRC \ varPhi（b） - \ varPhi（b）\ varPhi的（a）^ {*} \） （其中\（\ CIRC \）的特殊约旦关于产物\（\ mathcal {A} \）和\（\ mathcal {B}，\）），对于且仅当\（\ varPhi \）是\（* \） - ring时，对于所有元素\（a，b \ in \ mathcal {A} \）同构。特别是如果冯·诺依曼代数\（\ mathcal {A} \）和\（\ mathcal {B} \）是I型因子，则\（\ varPhi \）是a同构或共轭unit同构。