Peripherally automorphic unital completely positive maps

Abstract

We identify and characterize unital completely positive (UCP) maps on finite dimensional $C^{\ast }$-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 $C^{\ast }$-algebras with spectrum contained in the unit circle are $\ast$-automorphisms.

16 pages

Cited by in corpus (2)

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