Order-Preserving Variants of The Basic Principles of Functional Analysis

TL;DR

This paper develops order-preserving variants of fundamental theorems in functional analysis, extending classical results like Hahn-Banach and Banach-Alaoglu to ordered structures.

Contribution

It introduces order-preserving versions of key functional analysis principles, providing new tools for analysis in ordered spaces.

Findings

Order-preserving Hahn-Banach theorem established

Order-preserving Banach-Steinhaus theorem proven

Order-preserving Banach-Alaoglu theorem demonstrated

Abstract

We established order-preserving versions of the basic principles of functional analysis such as Hahn-Banach, Banach-Steinhaus, open mapping and Banach-Alaoglu theorems.