From geometry to invertibility preservers

TL;DR

This paper characterizes bijections on matrix and operator spaces that preserve the invertibility of differences between pairs, providing a comprehensive understanding of invertibility-preserving transformations.

Contribution

It offers a complete characterization of invertibility difference preservers on matrix and operator algebras, extending previous results.

Findings

Identifies all bijections preserving invertibility of differences in both directions.

Provides a structural description of such invertibility-preserving maps.

Extends known results from matrices to operator algebras.

Abstract

We characterize bijections on matrix spaces (operator algebras) preserving full rank (invertibility) of differences of matrix (operator) pairs in both directions.