A new look at the Hardy-Littlewood-P\'{o}lya inequality of majorization

TL;DR

This paper extends the Hardy-Littlewood-Pólya majorization inequality to ordered Banach spaces, broadening its applicability and providing new insights into the structure of these spaces.

Contribution

The paper introduces a novel extension of the Hardy-Littlewood-Pólya inequality to ordered Banach spaces, with multiple applications demonstrating its utility.

Findings

Extended the inequality to ordered Banach spaces

Provided several applications of the extended inequality

Enhanced understanding of majorization in Banach space context

Abstract

The Hardy-Littlewood-P\'{o}lya inequality of majorization is extended to the framework of ordered Banach spaces. Several applications illustrating our main results are also included.