Journal of the
Korean Mathematical Society JKMS

In this note, compound-commuting additive maps on matrix spaces are studied. We show that compound-commuting additive maps send rank one matrices to matrices of rank less than or equal to one. By using the structural results of rank-one nonincreasing additive maps, we characterize compound-commuting additive maps on four types of matrices: triangular matrices, square matrices, symmetric matrices and Hermitian matrices.

Keywords: rank, compound matrix, compound-commuting additive map, rank-one nonincreasing additive map

MSC numbers: 15A03, 15A04