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Choquet order and hyperrigidity for function systems. (arXiv:1608.02334v2 [math.OA] UPDATED)

来源于:arXiv
We establish a new characterization of the Choquet order on the space of probability measures on a compact convex set. This characterization is dilation-theoretic, meaning that it relates to the representation theory of positive linear maps on the C*-algebra of continuous functions on the set. We develop this connection between Choquet theory and the theory of operator algebras, and utilize it to establish Arveson's hyperrigidity conjecture for function systems. This yields a significant strengthening of \v{S}a\v{s}kin's approximation theorem for positive maps on commutative C*-algebras that is valid in the non-metrizable setting and does not require the range of the maps to be commutative. We also obtain an extension of Cartier's theorem on dilation of measures that is valid in the non-metrizable setting. 查看全文>>