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arXiv · 2212.07351

Peripherally automorphic unital completely positive maps

B. V. Rajarama Bhat·Samir Kar·Bharat Talwar
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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 $\ast$-automorphisms.

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B. V. Rajarama Bhat, Samir Kar, Bharat Talwar. 2022-12-14. Peripherally automorphic unital completely positive maps. https://doi.org/10.1016/j.laa.2023.08.020

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