Linear preservers of weak majorization on ℓp(I)+, when p ∈ (1,∞)

We present a necessary and sufficient conditions that a bounded linear map on ℓp(I)ℓp(I), when p∈(1,∞)p∈(1,∞), may be considered as a linear preserver of weak majorization on ℓp(I)+ℓp(I)+, where I is an arbitrary infinite set. We also prove that the class of all linear preservers of weak majorization is closed under the norm topology.