Аңдатпа
We identify and characterize unital completely positive (UCP) maps on finite dimensional C ⁎ -algebras for which the Choi-Effros product extended to the space generated by peripheral eigenvectors matches with the original product. We analyze a decomposition of general UCP maps in finite dimensions into persistent and transient parts. It is shown that UCP maps on finite dimensional C ⁎ -algebras with spectrum contained in the unit circle are ⁎-automorphisms.