因子von Neumann代数上完全保~*-Jordan零积的映射的研究

The Study of Maps Completely Preserving ~*-Jordan Zero-Products on Factor von Neumann Algebras

为了研究因子von Neumann代数上完全保~*-Jordan零积的满射的刻画问题,依据双边完全保~*-Jordan零积和双边2-保~*-Jordan零积的定义,采用完全保持的方法,证明了如果Φ是von Neumann代数A到B的一个满射,则Φ是线性或共轭线性~*-同构的非零常数倍。

In order to characterize the maps completely preserving*-Jordan zero-products on factor von Neumann algebras,according to the definition of bilateral complete preserving*-Jordan zero-products and bilateral2-preserving*-Jordan zero-products,taking a completely preserve approach,it is proved that ifΦis a surjection of von Neumann algebra A to B,thenΦis the non-zero scalar multiple of linear or conjugate linear*-isomorphism.