Abstract
Let $S$ be an operator system in $B(H)$ and let $A$ be its generated $C^{*}$-algebra. We give a new characterization of Arveson’s unique extension property for unital completely positive maps on $S$. We also show that when $A$ is a Type I $C^{\ast}$-algebra, if every irreducible representation of $A$ is a boundary representation for $S$, then every unital completely positive map on $A$ with codomain $A"$ that fixes $S$ also fixes $A$.
Citation
Craig Kleski. "Korovkin-type properties for completely positive maps." Illinois J. Math. 58 (4) 1107 - 1116, Winter 2014. https://doi.org/10.1215/ijm/1446819304
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