矩阵算子代数上的完全正映射

Completely positive maps on matrix operator algebras

证明了二阶矩阵 C* 代数之间 *同构在满足辛群作用不变性时可表示为 C* 代数间的两个 *同构的直和 ,同时给出了矩阵 C*代数的一些类似数值矩阵的性质 .通过证明完全正映射的一个类似于 Krein- Milman定理的性质 ,给出了一个纯的完全正映射延拓的存在性证明 .

It is proved that a * isomorphism between second order matrix C * algelas which satisfies symplectic group invariant conditions can be expressed as direct sum of two * isomorphism.Some properties of matrix C * algebras similar to scalar matrix are given.By proving a character of completely positive maps similar to Krein Milman theorem ,the existence of the extension of pure completely positive maps is proved.