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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>>