因子上保持混合三重η-积的非线性映射

Nonlinear maps preserving mixed triple η-products between factors

令η∈C{0,-1},设φ是两个因子上的不必为线性的双射并且满足φ(I)=I,如果?保持混合三重η-积,那么当η不是实数时?是线性*-同构;当η是实数时φ是线性*-同构或共轭线性*-同构。

Let η∈C{0,-1}and let φ be a not necessarily linear bijection between two factors, satisfying φ(I)=I and preserving mixed triple η-product. It is showed that ? is a linear *-isomorphism if η is not real and φ is either a linear *-isomorphism or a conjugate linear *-isomorphism if η is real.