Isomorphisms of Birkhoff-James orthogonality on finite-dimensional $C^*$-algebra

TL;DR

This paper classifies bijective maps that strongly preserve Birkhoff-James orthogonality in finite-dimensional complex $C^*$-algebras, revealing their near-isometric and real-linear structure.

Contribution

It provides a complete classification of orthogonality-preserving bijections in finite-dimensional $C^*$-algebras, detailing their structure and properties.

Findings

Maps are close to real-linear isometries

Structure of orthogonality-preserving maps is characterized

Classification applies to finite-dimensional complex $C^*$-algebras

Abstract

We classify bijective maps which strongly preserve Birkhoff-James orthogonality on a finite-dimensional complex $C^*$-algebra. It is shown that those maps are close to being real-linear isometries whose structure is also determined.