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Friday, April 10, 2015

**Abstract:** Korovkin's theorem inspired much research in approximation theory and functional analysis, and it invites a generalization to noncommutative function spaces. In this talk, we will review the classic theorem for positive maps on the continuous functions on the unit interval. We then generalize these notions to operator systems, and prove a noncommutative version of Saskin's theorem on the connection between Korovkin sets and Choquet boundaries. Finally, we discuss a conjecture of Arveson and progress towards its solution.