Weak majorization and doubly substochastic operators on l(p)(I)

Author:

Ljubenovic, Martin  

Journal:

LINEAR ALGEBRA AND ITS APPLICATIONS

Issue Date:

2015

Abstract(summary):

We extend the notion of weak majorization on the Banach space l(p)(I), where I is a non-empty set and p is an element of [1, infinity), using doubly substochastic operators on l(p) (I). The close relationship between weak majorization and these operators are presented. Among others, we show that f <(w)g and g <(w) f, if there is a partial permutation P such that g =3D Pf. Using the specific type of positive increasing convex functions, a necessary and sufficient condition for f <(w) g and g <(w) f is given. (C) 2015 Elsevier Inc. All rights reserved.

Page:

295---316