Birkhoff-James classification of finite-dimensional $C^{\ast }$-algebras

Abstract

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

arXiv commentAccepted for publication in Proc. Amer. Math. Soc