完全保持不同因子交换性的映射

Maps Completely Preserving Commutativity up to a Factor on Standard Operator Algebras

刻画了实或复的无限维Banch空间上的标准算子代数间完全保持不同因子交换性的一般映射,证明了这样的映射是同构的常数倍或(复的情形下)共轭同构的常数倍。

This paper gives a characterization of surjections between A and B which completely preserves commuta-tivity up to a factor in both directions,which shows that every map completely preserving commutativity up to a fac-tor from A onto B is a scalar multiple of either an isomorphism or( in the complex case)a conjugate isomorphism.