On partial orders of operators

TL;DR

This paper explores different partial orders on operators, clarifies their relationships, and introduces a new unified order to better understand and compare these operator orders.

Contribution

It provides characterizations of existing operator orders and introduces a new partial order that unifies the study of these orders.

Findings

Characterizations of star, minus, and diamond orders in various contexts

A new partial order that unifies the existing orders

Enhanced understanding of relationships between different operator orders

Abstract

Characterizations of the star, minus and diamond orders of operators are given in various contexts and the relationship between these orders is made more transparent. Moreover, we introduce a new partial order of operators which provides a unified scenario for studying the other three orders.