Linear preservers of circulant majorization on Mn

Let Mn be the set of all n × n matrices with real entries. We say that C ∈ Mn is circulant matrix majorized by D ∈ Mn and write C ≺c D, if C = QD for some circulant doubly stochastic matrix Q ∈ Mn. A linear operator T : Mn  Mn is said to be a preserver of ≺c, if TC ≺c TD whenever C ≺c D for C,D ∈ Mn. The main purpose of this paper is to characterize the linear preservers of ≺c from Mn to Mn