A note on k-potence preserving maps Original Research Article

Let Mn be the algebra of all n×n complex matrices and Γn the set of all k-potent matrices in Mn. Suppose phi:Mn→Mn is a map satisfying A-λBset membership, variantΓn implies phi(A)-λphi(B)set membership, variantΓn, where A, Bset membership, variantMn, image. Then either phi is of the form phi(A)=cTAT-1, Aset membership, variantMn, or phi is of the form phi(A)=cTAtT-1, Aset membership, variantMn, where Tset membership, variantMn is an invertible matrix, image satisfies ck=c.