Special classes of positive and completely positive maps
Many authors have studied the problem of characterising the positive and completely positive maps on square complex matrices of size \(n\) under certain invariant conditions. These authors have characterized the above mentioned maps that leave invariant the diagonal or the \(k\)th elementary symmetric functions of the diagonal entries, for \(1 < k \leq n.\) The case \(k=1\) corresponding to the trace function has already been studied by different authors. Here the authors also show that such a positive map is always decomposable if \(n \leq 3\) but fails for \(n > 3.\) The results for the real case are deduced from the complex case which requires minor modifications.
scientific article; zbMATH DE number 999974