Positive linear maps between matrix algebras which fix diagonals

AbstractWe consider a class of positive linar maps from the n-dimensional matrix algebra into itself which fix diagonal entries. We show that they are expressed by Hadamard products, and study their decompositions into the sums of completely positive linear maps and completely copositive linear maps. In the three-dimensional case, we show that every positive linear map in this type is decomposable, and give an intrinsic characterization for the positivity of these maps when the involving coefficients are real numbers