标准算子代数上完全保斜幂等性的可加映射

Additive Maps Completely Preserving Skew Idempotency Between Standard Operator Algebras

在完全保持幂等性映射研究的基础上,利用算子代数的方法讨论了无限维实或复Banach空间上的标准算子代数上完全保持幂等性的可加映射的刻画问题.通过将问题划归为秩-幂等元集上双边保持零积的映射的刻画问题,证明了标准算子代数上完全保持斜幂等性的可加映射是同构或(复情形)共轭同构.

On the basis of studying the completely preserving idempotency maps and by using the method of operator algebra,additive maps of completely preserving skew idempotency between standard operator algebras on real or complex infinite dimensional Banach spaces was discussed.By means of the conversion from the above problems to ones of maps preserving zero sets on rank one idempotent sets,it is proved that all the completely preserving skew idempotency additive maps between standard operator algebras are isomorphism or（in the complex case） conjugate-isomorphism.