Linear preservers of weak majorization on ℓ1(I)+, when I is an infinite set

The necessary and sufficient conditions that a bounded linear map on the Banach space ℓ1(I), may be considered as a linear preserver of weak majorization on ℓ1(I)+, where I is an arbitrary infinite set, are given. Also, we prove that the set of all linear preservers of weak majorization is closed under the norm topology.