Convex majorization on discrete ℓpℓp spaces

In this paper for p∈[1,+∞)p∈[1,+∞) and a nonempty set I  , we consider a natural preorder on ℓp(I)ℓp(I), which is said to be “convex majorization”. Then some interesting properties of all bounded linear operators T:ℓp(I)→ℓp(I)T:ℓp(I)→ℓp(I), preserving the convex majorization, are given. We also characterize these operators and assert one of the important properties of them, that is, the rows of matrix form of such an operator belongs to ℓ1(I)ℓ1(I).