Abstract
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.
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