完全保持斜Lie零积的映射

Maps of Completely Preserving Skew Lie Zero Products

对Hilbert空间上的投影算子上双边保正交性的双射的刻画,得到了复无限维Hilbert空间上的~*-标准算子代数之间完全保持斜Lie零积的满射的具体结构形式,进而证明了这样的映射是同构或者共轭同构的常数倍。

By characterizing the bijective maps preserving orthogonality in both directions on the projectionoperators on the Hilbert spaces, the characterization of surjective maps completely preserving skew Lie zero products on ＊ -standard operator algebras on infinite complex Hilbert spaces are obtained, and the maps are proved to be either an isomorphism or a conjugate isomorphism.