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Application of Jacobi's representation theorem to locally multiplicatively convex topological R-algebras

Application of Jacobi's representation theorem to locally multiplicatively convex topological R-algebras

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GHASEMI, Mehdi, Salma KUHLMANN, Murray MARSHALL, 2014. Application of Jacobi's representation theorem to locally multiplicatively convex topological R-algebras. In: Journal of Functional Analysis. 266(2), pp. 1041-1049. ISSN 0022-1236. eISSN 1096-0783

@article{Ghasemi2014Appli-26398, title={Application of Jacobi's representation theorem to locally multiplicatively convex topological R-algebras}, year={2014}, doi={10.1016/j.jfa.2013.09.001}, number={2}, volume={266}, issn={0022-1236}, journal={Journal of Functional Analysis}, pages={1041--1049}, author={Ghasemi, Mehdi and Kuhlmann, Salma and Marshall, Murray} }

2014-02-18T12:54:50Z Marshall, Murray Journal of Functional Analysis ; 266 (2014), 2. - S. 1041-1049 2014-02-18T12:54:50Z Let A be a commutative unital RR-algebra and let ρ be a seminorm on A which satisfies ρ(ab)⩽ρ(a)ρ(b)ρ(ab)⩽ρ(a)ρ(b). We apply T. Jacobi's representation theorem to determine the closure of a ∑A<sup>2d</sup>-module S of A in the topology induced by ρ, for any integer d⩾1d⩾1. We show that this closure is exactly the set of all elements a∈Aa∈A such that α(a)⩾0α(a)⩾0 for every ρ-continuous RR-algebra homomorphism α:A→Rα:A→R with α(S)⊆[0,∞)α(S)⊆[0,∞), and that this result continues to hold when ρ is replaced by any locally multiplicatively convex topology τ on A. We obtain a representation of any linear functional L:A→RL:A→R which is continuous with respect to any such ρ or τ and nonnegative on S as integration with respect to a unique Radon measure on the space of all real-valued RR-algebra homomorphisms on A, and we characterize the support of the measure obtained in this way. eng Application of Jacobi's representation theorem to locally multiplicatively convex topological R-algebras Kuhlmann, Salma Marshall, Murray deposit-license 2014 Ghasemi, Mehdi Kuhlmann, Salma Ghasemi, Mehdi

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