Abstract
In this paper, we study the local ordered \(*\)-vector spaces and their representations. We prove that each Archimedean local ordered \(*\)-vector space, can be represented as a \(*\)-vector subspace of C(X), for some completely Hausdorff compactly generated space X. Furthermore, we show that for every Archimedean local ordered \(*\)-vector space V, there is a representation of V into the \(*\)-algebra of all noncommutative continuous functions on a quantum domain \({\mathcal {E}}\) such that the quantum order induced by this representation is the minimal quantum system structure on V.
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Acknowledgements
The authors would like to thank the referee for the constructive comments which will definitely improve the quality of the manuscript. Also, we are specially thankful to Prof. A.A. Dosi for sending us his recent manuscript [6]. The research of the first author was in part supported by a Grant from IPM (No. 98460119).
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Asadi, M.B., Hassanpour-Yakhdani, Z. & Shamloo, S. A locally convex version of Kadison’s representation theorem. Positivity 24, 1449–1460 (2020). https://doi.org/10.1007/s11117-020-00740-2
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DOI: https://doi.org/10.1007/s11117-020-00740-2