## “School of Mathematics”

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Paper   IPM / M / 16011
 School of Mathematics Title: A locally convex version of Kadison 's representation theorem Author(s): Mohammad Bagher Asadi (Joint with Z. Hassanpour-Yakhdani and S. Shamloo) Status: To Appear Journal: Positivity Supported by: IPM
Abstract:
In this paper, we study the local ordered ï¿½??-vector spaces and their representations. We prove that each Archimedean local orderedï¿½??-vector space, can be represented as a ï¿½??-vector subspace of C(X), for some completely Hausdorï¿½? compactly generated space X. Furthermore, we show that for every Archimedean local ordered ï¿½??-vector space V , there is a representation of V into the ï¿½??-algebra of all noncommutative continuous functions on a quantum domain E such that the quantum order induced by this representation is the minimal quantum system structure on V .

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