标准算子代数上完全保立方零元的可加映射

Additive Maps Completely Preserving Cube-zero Operators on Standard Operator Algebras

引用对Banach空间上的一秩幂等元集上双边保Jordan三重零积的满射的刻画,得到了实或复无限维Banach空间上的标准算子代数之间完全保持立方零元的可加满射的具体结构形式,进而证明了这样的映射是同构或者(复情形下)共轭同构。

By characterizing the surjective maps preserving the zero triple Jordan product in both directions on the set of all rank-one idempotents of a Banach space, we obtain the characterization of additive surjections completely preserving cube-zero operators on standard operator algebras on infinite dimensional real or complex Banach spaces, and then prove that the maps are either an isomorphism or （in the complex case）a conjugate isomorphism.