By the Choi matrix criteria it is easy to determine if a specific linear matrix map is completely positive, but to establish whether a linear matrix map is positive is much less straightforward. In this paper we consider classes of linear matrix maps, determined by structural conditions on an associated matrix, for which positivity and complete positivity coincide. The basis of our proofs lies in a representation of ⁎-linear matrix maps going back to work of R.D. Hill which enables us to formulate a sufficient condition in terms of surjectivity of certain bilinear maps.

中文翻译：

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正性和完全正性重合的线性矩阵图

通过 Choi 矩阵标准，很容易确定特定线性矩阵图是否完全为正，但确定线性矩阵图是否为正则不那么直接。在本文中，我们考虑由相关矩阵上的结构条件确定的线性矩阵映射类别，对于它们，正性和完全正性是一致的。我们证明的基础在于 ⁎ 线性矩阵映射的表示，这可以追溯到 RD Hill 的工作，这使我们能够根据某些双线性映射的满射性来制定充分条件。