Birkhoff-James classification of finite-dimensional $C^*$-algebras

TL;DR

This paper classifies finite-dimensional $C^*$-algebras over real or complex fields using Birkhoff-James orthogonality properties and explores preservers of strong orthogonality.

Contribution

It introduces a classification method for finite-dimensional $C^*$-algebras based on Birkhoff-James orthogonality properties, including applications to orthogonality preservers.

Findings

Classification of finite-dimensional $C^*$-algebras using orthogonality properties

Characterization of strong Birkhoff-James orthogonality preservers

Insights into the structure of $C^*$-algebras via orthogonality

Abstract

We classify real or complex finite-dimensional $C^*$-algebras and their underlying fields from the properties of Birkhoff-James orthogonality. Application to strong Birkhoff-James orthogonality preservers is also given.