Partial isometries in an absolute order unit space

TL;DR

This paper generalizes orthogonality and introduces partial isometries within absolute matrix order unit spaces, providing new insights into the structure and comparison of order projections.

Contribution

It extends the concept of orthogonality to all elements and defines partial isometries in this setting, advancing the understanding of order projections.

Findings

Extended orthogonality to general elements.

Introduced partial isometries in absolute matrix order unit spaces.

Analyzed the comparison and finiteness of order projections.

Abstract

In this paper, we extend the notion of orthogonality to the general elements of an absolute matrix order unit space and relate it to the orthogonality among positive elements. We introduce the notion of a partial isometry in an absolute matrix order unit space. As an application, we describe the comparison of order projections. We also discuss finiteness of order projections.