一秩元集上完全保反对合性的可加映射

Additive Maps Completely Preserving Anti-involution on Set of Rank One Operators

主要刻画了一秩元集上完全保反对合性的可加映射,证明了这样的映射是同构的常数倍或(复情形下)共轭同构的常数倍。对于映射Φ∶R→,对于每个n∈瓔,定义映射Φn为Φn((sij)n×n)=(Φ(sij))n×n.则如果Φn保反对合性,称Φ是n-保反对合性的;如果对于每个正整数n,Φ是n-保反对性的,则称Φ是完全保反对合性的。

Additive maps between the sets of rank-one operators completely preserving anti-involution are characterized,and such maps are proved to be an constant times of isomorphisms or（in the complex case）conjugate isomorphisms.To map Φ∶ R→χ and each n ∈N,a map Φn is defined as Φn（（sij）n×n）=（Φ（sij））n×n.If Φn preserves anti-involution,Φ is n-anti-involution preserving.And if Φ is n-anti-involution preserving for every positive integer n,Φ is completely anti-involution preserving.