von Neumann 数上保持半*-Jordan积的映射

摘要

设M和N是yon Neumann代数没有type Ⅰ 1中心直和项,p是M到N的双射.证明Φ保持半*-Jordan积,即Φ(TS+ST*)=Φ(T)Φ(S)+Φ(S)Φ(T)* (V)T,S∈M),则Φ是可加映射.%Let M and N be von Neumann algebras and Φ be a bijective map from M onto N.It is proved that Φ preserves semi *-Jordan product,that is Φ(TS+ST*)=Φ(T) Φ(S) +Φ(S) Φ(T)* (∨) T,S∈M,then Φ is additive maps.