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

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.