Mathematics – Operator Algebras
Scientific paper
2008-04-22
Journal of Geometry and Physics 59 (2009), pp. 861-875
Mathematics
Operator Algebras
31 pages. To appear in Journal of Geometry and Physics
Scientific paper
In this paper we put forward the definition of particular subsets on a unital C*-algebra, that we call isocones, and which reduce in the commutative case to the set of continuous non-decreasing functions with real values for a partial order relation defined on the spectrum of the algebra, which satisfies a compatibility condition with the topology (complete separateness). We prove that this space/algebra correspondence is a dual equivalence of categories, which is in fact only a mild generalization of the Gelfand-Naimark duality. Thus we can expect that general isocones could serve to define a notion of noncommutative ordered spaces. We also explore some basic algebraic constructions involving isocones, and classify those which are defined in M_2(C).
Besnard Fabien
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