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Closure of the cone of sums of 2d-powers in real topological algebras

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GHASEMI, Mehdi, Salma KUHLMANN, 2013. Closure of the cone of sums of 2d-powers in real topological algebras. In: Journal of Functional Analysis. 264(1), pp. 413-427. ISSN 0022-1236. eISSN 1096-0783. Available under: doi: 10.1016/j.jfa.2012.10.018

@article{Ghasemi2013Closu-21247, title={Closure of the cone of sums of 2d-powers in real topological algebras}, year={2013}, doi={10.1016/j.jfa.2012.10.018}, number={1}, volume={264}, issn={0022-1236}, journal={Journal of Functional Analysis}, pages={413--427}, author={Ghasemi, Mehdi and Kuhlmann, Salma} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dc:date rdf:datatype="">2013-01-25T10:40:54Z</dc:date> <dcterms:isPartOf rdf:resource=""/> <dc:rights>terms-of-use</dc:rights> <dc:creator>Ghasemi, Mehdi</dc:creator> <dcterms:title>Closure of the cone of sums of 2d-powers in real topological algebras</dcterms:title> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:issued>2013</dcterms:issued> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:bibliographicCitation>Journal of Functional Analysis ; 264 (2013), 1. - S. 413-427</dcterms:bibliographicCitation> <dcterms:abstract xml:lang="eng">Let R be a unitary commutative R-algebra and K⊆X(R)=Hom(R,R), closed with respect to the product topology. We consider R endowed with the topology T(K), induced by the family of seminorms ρα(a):=|α(a)|, for α∈K and a∈R. In case K is compact, we also consider the topology induced by ‖a‖K:=supα∈K|α(a)| for a∈R. If K is Zariski dense, then those topologies are Hausdorff. In this paper we prove that the closure of the cone of sums of 2d-powers, ∑R2d, with respect to those two topologies is equal to Psd(K):={a∈R:α(a)⩾0, for all α∈K}. In particular, any continuous linear functional L on the polynomial ring View the MathML source with L(h2d)⩾0 for each View the MathML source is integration with respect to a positive Borel measure supported on K. Finally we give necessary and sufficient conditions to ensure the continuity of a linear functional with respect to those two topologies.</dcterms:abstract> <dcterms:rights rdf:resource=""/> <dc:contributor>Ghasemi, Mehdi</dc:contributor> <dspace:isPartOfCollection rdf:resource=""/> <dc:language>eng</dc:language> <dc:contributor>Kuhlmann, Salma</dc:contributor> <dcterms:available rdf:datatype="">2013-01-25T10:40:54Z</dcterms:available> <dc:creator>Kuhlmann, Salma</dc:creator> <bibo:uri rdf:resource=""/> </rdf:Description> </rdf:RDF>

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