Illinois Journal of Mathematics

Korovkin-type properties for completely positive maps

Craig Kleski

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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 $A$.

Article information

Illinois J. Math., Volume 58, Number 4 (2014), 1107-1116.

Received: 10 January 2015
Revised: 2 April 2015
First available in Project Euclid: 6 November 2015

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Zentralblatt MATH identifier

Primary: 41A36: Approximation by positive operators 46L07: Operator spaces and completely bounded maps [See also 47L25] 46L52: Noncommutative function spaces 47A20: Dilations, extensions, compressions


Kleski, Craig. Korovkin-type properties for completely positive maps. Illinois J. Math. 58 (2014), no. 4, 1107--1116. doi:10.1215/ijm/1446819304.

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