Linear matrix maps for which positivity and complete positivity coincide

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