Geodesic
A Representation Theorem for Archimedean Quadratic Modules on ∗-Rings
Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 39-52

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DOI

We present a new approach to noncommutative real algebraic geometry based on the representation theory of ${{C}^{*}}$ -algebras. An important result in commutative real algebraic geometry is Jacobi's representation theorem for archimedean quadratic modules on commutative rings. We show that this theorem is a consequence of the Gelfand–Naimark representation theorem for commutative ${{C}^{*}}$ -algebras. A noncommutative version of Gelfand–Naimark theory was studied by I. Fujimoto. We use his results to generalize Jacobi's theorem to associative rings with involution.
DOI : 10.4153/CMB-2009-005-4
Mots-clés : 16W80, 46L05, 46L89, 14P99, Ordered rings with involution, C*-algebras and their representations, noncommutative convexity theory, real algebraic geometry 
Cimprič, Jakob. A Representation Theorem for Archimedean Quadratic Modules on ∗-Rings. Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 39-52. doi: 10.4153/CMB-2009-005-4
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     title = {A {Representation} {Theorem} for {Archimedean} {Quadratic} {Modules} on {\ensuremath{*}-Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {39--52},
     year = {2009},
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     doi = {10.4153/CMB-2009-005-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-005-4/}
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