On Row-Sum Majorization

Let M n , m be the set of all n × m real or complex matrices. For A, B ∈ M n , m , we say that A is row-sum majorized by B (written as A ≺ rs B ) if R ( A ) ≺ R ( B ), where R ( A ) is the row sum vector of A and ≺ is the classical majorization on ℝ n . In the present paper, the structure of all linear operators T : M n , m → M n , m preserving or strongly preserving row-sum majorization is characterized. Also we consider the concepts of even and circulant majorization on ℝ n and then find the linear preservers of row-sum majorization of these relations on M n , m .