Minus partial order and linear preservers

TL;DR

This paper explores the minus partial order in unital rings, generalizing known matrix results and examining linear maps that preserve this order in specific Banach algebra contexts.

Contribution

It extends properties of the minus partial order from matrices to unital rings and analyzes order-preserving linear maps in semisimple Banach algebras.

Findings

Generalized results for matrices to unital rings

Characterized linear maps preserving the minus partial order

Connected properties in Banach algebra settings

Abstract

In this paper we investigate the properties of minus partial order in unital rings. We generalize several results well known for matrices and bounded linear operators on Banach spaces. We also study linear maps preserving the minus partial order in unital semisimple Banach algebras with essential socle.