Projections in an order unit space and orthogonality

TL;DR

This paper introduces and characterizes order projections in order unit spaces using orthogonality, and explores their structure when an order unit is added to a normed linear space.

Contribution

It defines order projections via the order unit property and characterizes them through orthogonality, expanding understanding of their structure in order unit spaces.

Findings

Order projections are characterized by orthogonality.

Order projections in extended spaces are described explicitly.

The paper provides a geometric perspective on projections in order unit spaces.

Abstract

We introduce the notion of order projections using the order unit property of a positive element in an order unit space and characterize them in terms of (geometric) orthogonality. We describe order projections of the order unit space obtained by adjoining an order unit to a normed linear space.