Maps on upper-triangular matrix algebras preserving k-potences Original Research Article

Let Mn be the space of all n×n complex matrices and Tn the subset of Mn consisting of all upper-triangular matrices. Denote by Γn the subset of Mn consisting of all n×n k-potent matrices, TΓn the subset of Γn consisting of all upper-triangular matrices. In this paper we describe the map phi:Tn→Mn satisfying A-λBset membership, variantTΓn if and only if phi(A)-λphi(B)set membership, variantΓn for every A,Bset membership, variantTn and λset membership, variantC.