Publikation: A Nichtnegativstellensatz for polynomials in noncommuting variables
Lade...
Dateien
Datum
2007
Autor:innen
Herausgeber:innen
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Schriftenreihe
Auflagebezeichnung
URI (zitierfähiger Link)
DOI (zitierfähiger Link)
Internationale Patentnummer
Link zur Lizenz
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Open Access Green
Sammlungen
Core Facility der Universität Konstanz
Titel in einer weiteren Sprache
Publikationstyp
Zeitschriftenartikel
Publikationsstatus
Published
Erschienen in
Israel Journal of Mathematics. 2007, 161(1), pp. 17-27. ISSN 0021-2172. Available under: doi: 10.1007/s11856-007-0070-2
Zusammenfassung
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.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
noncommutative polynomials, Nichtnegativstellensatz, sums of squares, semialgebraic sets, contractive operators.
Konferenz
Rezension
undefined / . - undefined, undefined
Zitieren
ISO 690
KLEP, Igor, Markus SCHWEIGHOFER, 2007. A Nichtnegativstellensatz for polynomials in noncommuting variables. In: Israel Journal of Mathematics. 2007, 161(1), pp. 17-27. ISSN 0021-2172. Available under: doi: 10.1007/s11856-007-0070-2BibTex
@article{Klep2007Nicht-15642,
year={2007},
doi={10.1007/s11856-007-0070-2},
title={A Nichtnegativstellensatz for polynomials in noncommuting variables},
number={1},
volume={161},
issn={0021-2172},
journal={Israel Journal of Mathematics},
pages={17--27},
author={Klep, Igor and Schweighofer, Markus}
}RDF
<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/server/rdf/resource/123456789/15642">
<dc:contributor>Klep, Igor</dc:contributor>
<dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-11-09T10:37:00Z</dcterms:available>
<dc:language>eng</dc:language>
<dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
<dcterms:issued>2007</dcterms:issued>
<dc:creator>Klep, Igor</dc:creator>
<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>
<dcterms:title>A Nichtnegativstellensatz for polynomials in noncommuting variables</dcterms:title>
<dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-11-09T10:37:00Z</dc:date>
<dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/15642/2/nirgends.pdf"/>
<dc:contributor>Schweighofer, Markus</dc:contributor>
<dc:rights>terms-of-use</dc:rights>
<dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/15642/2/nirgends.pdf"/>
<void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
<bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/15642"/>
<dcterms:bibliographicCitation>First publ. in: Israel Journal of Mathematics ; 161 (2007), 1. - S. 17-27</dcterms:bibliographicCitation>
<dc:creator>Schweighofer, Markus</dc:creator>
<dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
<dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
<foaf:homepage rdf:resource="http://localhost:8080/"/>
</rdf:Description>
</rdf:RDF>Interner Vermerk
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Prüfungsdatum der Dissertation
Finanzierungsart
Kommentar zur Publikation
Allianzlizenz
Corresponding Authors der Uni Konstanz vorhanden
Internationale Co-Autor:innen
Universitätsbibliographie
Ja
