Additive preservers of mutual strong Birkhoff-James orthogonality on finite-dimensional $C^\ast$-algebras

TL;DR

This paper characterizes additive maps on finite-dimensional C*-algebras that preserve a specific orthogonality relation, providing a classification of such transformations.

Contribution

It offers a new classification of additive surjections preserving mutual strong Birkhoff-James orthogonality in finite-dimensional C*-algebras.

Findings

Characterization of additive surjections preserving singularity in one direction.

Classification of additive surjections preserving mutual strong Birkhoff-James orthogonality.

Abstract

We describe additive surjections on direct sum of matrix algebras that preserve singularity in one direction. As an application, we classify additive surjections on finite-dimensional $C^\ast$-algebras that preserve mutual strong Birkhoff-James orthogonality in one direction.