Some properties of operators preserving convex majorization on discrete ℓpℓp spaces

In this paper we consider recent work linking “convex majorization” and isotonic operators on ℓp(I)ℓp(I), where I   is assumed to be an infinite set and p∈[1,+∞)p∈[1,+∞). We proved that PcPc, the set of all isotonic operators on ℓp(I)ℓp(I) is closed. We also provided some other properties about isotonic operators.