Linear preservers of majorization on lp(I)

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Abstract

In this paper we use doubly stochastic operators to extend the notion of majorization on lp, where I is assumed to be an infinite set and p(1,+), and then characterize the structure of all bounded linear maps on this space which preserve majorization. We will see that the two cases p(1,+) and p=1 lead to different structures.

AMS classification

15A86
47B60

Keywords

Majorization
Linear preserver
Permutation
Doubly stochastic operator

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This work is partially supported by a grant from Isfahan University of Technology.