Real operator algebras and real positive maps

TL;DR

This paper develops foundational aspects of real operator algebras and real Jordan operator algebras, emphasizing real positivity and morphisms, extending previous complex scalar results to the real setting.

Contribution

It introduces a foundational framework for real operator and Jordan algebras, incorporating real positivity and morphisms, building on prior complex scalar work.

Findings

Established basic properties of real operator algebras

Extended real positivity concepts to the real scalar setting

Analyzed morphisms between real operator algebras

Abstract

We present some foundations for a theory of real operator algebras and real Jordan operator algebras, and the various morphisms between these. A common theme is the ingredient of real positivity from papers of the first author with Read, Neal, Wang, and other coauthors, which we import to the real scalar setting here.