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A Nichtnegativstellensatz for polynomials in noncommuting variables

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KLEP, Igor, Markus SCHWEIGHOFER, 2007. A Nichtnegativstellensatz for polynomials in noncommuting variables. In: Israel Journal of Mathematics. 161(1), pp. 17-27. ISSN 0021-2172. Available under: doi: 10.1007/s11856-007-0070-2

@article{Klep2007Nicht-15642, title={A Nichtnegativstellensatz for polynomials in noncommuting variables}, year={2007}, doi={10.1007/s11856-007-0070-2}, number={1}, volume={161}, issn={0021-2172}, journal={Israel Journal of Mathematics}, pages={17--27}, author={Klep, Igor and Schweighofer, Markus} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dc:creator>Schweighofer, Markus</dc:creator> <dspace:isPartOfCollection rdf:resource=""/> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:rights>terms-of-use</dc:rights> <dcterms:issued>2007</dcterms:issued> <dc:contributor>Klep, Igor</dc:contributor> <dcterms:hasPart rdf:resource=""/> <dcterms:isPartOf rdf:resource=""/> <dc:contributor>Schweighofer, Markus</dc:contributor> <dc:language>eng</dc:language> <dc:date rdf:datatype="">2011-11-09T10:37:00Z</dc:date> <dcterms:available rdf:datatype="">2011-11-09T10:37:00Z</dcterms:available> <dcterms:abstract xml:lang="eng">Helton recently proved that a symmetric polynomial in noncommuting variables is positive semidefinite on all bounded self-adjoint Hilbert space operators if and only if it is a sum of hermitian squares. We characterize the polynomials which are nowhere negative semidefinite on certain `bounded basic closed semialgebraic sets´ of bounded Hilbert space operators. The obtained representation for these polynomials involves multipliers analogous to the representation known from the classical commutative Positivstellensatz. It is still an open problem if a noncommutative version of Hilbert's 17th problem holds.</dcterms:abstract> <dc:creator>Klep, Igor</dc:creator> <dcterms:title>A Nichtnegativstellensatz for polynomials in noncommuting variables</dcterms:title> <dcterms:rights rdf:resource=""/> <dspace:hasBitstream rdf:resource=""/> <bibo:uri rdf:resource=""/> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:bibliographicCitation>First publ. in: Israel Journal of Mathematics ; 161 (2007), 1. - S. 17-27</dcterms:bibliographicCitation> </rdf:Description> </rdf:RDF>

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