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# Application of Jacobi's Representation Theorem to locally multiplicatively convex topological real Algebras

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GHASEMI, Mehdi, Salma KUHLMANN, Murray MARSHALL, 2012. Application of Jacobi's Representation Theorem to locally multiplicatively convex topological real Algebras

@unpublished{Ghasemi2012Appli-21264, title={Application of Jacobi's Representation Theorem to locally multiplicatively convex topological real Algebras}, year={2012}, author={Ghasemi, Mehdi and Kuhlmann, Salma and Marshall, Murray} }

<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/21264"> <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/21264"/> <dc:contributor>Ghasemi, Mehdi</dc:contributor> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dc:rights>terms-of-use</dc:rights> <dcterms:abstract xml:lang="eng">Let $A$ be a commutative unital $\mathbb{R}$-algebra and let $\rho$ be a seminorm on $A$ which satisfies $\rho(ab)\leq\rho(a)\rho(b)$. We apply T. Jacobi's representation theorem to determine the closure of a $\sum A^{2d}$-module $S$ of $A$ in the topology induced by $\rho$, for any integer $d\ge1$. We show that this closure is exactly the set of all elements $a\in A$ such that $\alpha(a)\ge0$ for every $\rho$-continuous $\mathbb{R}$-algebra homomorphism $\alpha : A \rightarrow \mathbb{R}$ with $\alpha(S)\subseteq[0,\infty)$, and that this result continues to hold when $\rho$ is replaced by any locally multiplicatively convex topology $\tau$ on $A$. We obtain a representation of any linear functional $L : A \rightarrow \reals$ which is continuous with respect to any such $\rho$ or $\tau$ and non-negative on $S$ as integration with respect to a unique Radon measure on the space of all real valued $\reals$-algebra homomorphisms on $A$, and we characterize the support of the measure obtained in this way.</dcterms:abstract> <dcterms:issued>2012</dcterms:issued> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:creator>Ghasemi, Mehdi</dc:creator> <dc:language>eng</dc:language> <dc:creator>Kuhlmann, Salma</dc:creator> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:contributor>Kuhlmann, Salma</dc:contributor> <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2013-01-28T10:16:55Z</dcterms:available> <dc:contributor>Marshall, Murray</dc:contributor> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2013-01-28T10:16:55Z</dc:date> <dcterms:title>Application of Jacobi's Representation Theorem to locally multiplicatively convex topological real Algebras</dcterms:title> <dc:creator>Marshall, Murray</dc:creator> <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/21264/1/ghasemi_212648.pdf"/> <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/21264/1/ghasemi_212648.pdf"/> </rdf:Description> </rdf:RDF>

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