Majorization on ℓ∞ and on its closed linear subspace c, and their linear preservers

In this paper, we extend the notion of majorization to ℓ∞, the Banach space of all bounded real sequences, and investigate some of its properties. Considering this notion on c, the subspace of all convergent real sequences, the structure of all bounded linear operators which preserve the majorization relation on this subspace is obtained. Finally we introduce two different classes of linear preservers of majorization on ℓ∞ which illustrate some important differences between the structure of these operators on ℓ∞ and those on ℓp spaces, for 1⩽p<∞, as well as those on c.