Special classes of positive and completely positive maps Original Research Article

Characterizations are given for the positive and completely positive maps on n × n complex matrices that leave invariant the diagonal entries or the kth elementary symmetric function of the diagonal entries, 1 < k less-than-or-equals, slant n. In addition, it is shown that such a positive map is always decomposable if n less-than-or-equals, slant 3, and this fails to hold if n > 3. The real case is also considered.