有限维张量积空间上的可分算子与PPT算子

Separable operators and PPT operators on a finite dimensional tensor product space

首先引入了张量积空间上的可分算子和PPT算子的定义,并给出了可分自伴算子、可分投影算子、可分半正定算子的标准形式,建立了可分算子与PPT算子的关系.进而定义了可分映射和PPT映射,并得到了一个可分映射保PPT算子的结论.

Separable operators and PPT operators on a finite dimensional tensor product space are intro‐duced .Then ,general forms of separable self‐adjoint operators ,separable projective operators and separa‐ble positive operators are obtained .The relationship between separable operators and PPT operators are proved ,and some examples w hich are PPT operators but not separable operators are given .Lastly ,sepa‐rable maps and PPT maps are introduced and discussed ,and it is proved that every separable map maps a PPT operator as a PPT operator .