Abstract
We extend the notion of weak majorization on the Banach space ℓp(I), where I is a non-empty set and p∈[1,∞), using doubly substochastic operators on ℓp(I). The close relationship between weak majorization and these operators are presented. Among others, we show that f≺wg and g≺wf, iff there is a partial permutation P such that g=Pf. Using the specific type of positive increasing convex functions, a necessary and sufficient condition for f≺wg and g≺wf is given.
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