关于正映射性质的注记  

Notes on the Properties of Positive Mappings

作　　者：禹鸥洋 任芳国[1] YU Ouyang;REN Fangguo(School of Mathematics and Statistics,Shaanxi Normal University,Xi’an 710119,China)

机构地区：[1]陕西师范大学数学与统计学院,西安710119

出　　处：《西安文理学院学报(自然科学版)》2024年第3期12-21,共10页Journal of Xi’an University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11471200)

摘　　要：利用矩阵谱范数及迹范数的性质、矩阵分解、半正定矩阵及分块半正定矩阵的性质和矩阵内积对正映射的性质进行更深入的研究,给出了三个紧凸集端点的特性刻画、获得正映射与其伴随映射的一些性质及完全正映射的一些刻画,这些结果充实了正映射的研究内容并为进一步讨论量子信息问题奠定了潜在的理论基础.By utilizing the properties of matrix spectral norms and trace norms,matrix decomposition,the properties of positive semi-definite matrices and block positive semi-definite matrices,as well as matrix inner product,a more in-depth study is conducted on the properties of positive mappings,the characterization of the endpoints of three compact convex sets,some properties of positive mappings and their adjoint mappings,and some characterizations of completely positive mappings are given,these results enrich the research content of positive mapping and lay a potential theoretical foundation for further discussion of quantum information problems.

关 键 词：分块矩阵 半正定矩阵 正映射 完全正映射 矩阵分解 

分 类 号：O151.21[理学—数学]