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.
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