The minus order and range additivity

TL;DR

This paper explores the minus order on bounded linear operators, characterizing it algebraically via range additivity, and applies these insights to generalized inverses, operator equations, and optimization problems.

Contribution

It provides a new algebraic characterization of the minus order using range additivity, enhancing understanding and applications in operator theory.

Findings

Minus order characterized by range additivity

Applications to generalized inverses of sums

Implications for operator equations and optimization

Abstract

We study the minus order on the algebra of bounded linear operators on a Hilbert space. By giving a characterization in terms of range additivity, we show that the intrinsic nature of the minus order is algebraic. Applications to generalized inverses of the sum of two operators, to systems of operator equations and to optimization problems are also presented.