A Nichtnegativstellensatz for polynomials in noncommuting variables
| dc.contributor.author | Klep, Igor | |
| dc.contributor.author | Schweighofer, Markus | |
| dc.date.accessioned | 2011-11-09T10:37:00Z | deu |
| dc.date.available | 2011-11-09T10:37:00Z | deu |
| dc.date.issued | 2007 | |
| dc.description.abstract | 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. | eng |
| dc.description.version | published | |
| dc.identifier.citation | First publ. in: Israel Journal of Mathematics ; 161 (2007), 1. - S. 17-27 | deu |
| dc.identifier.doi | 10.1007/s11856-007-0070-2 | deu |
| dc.identifier.ppn | 352871083 | deu |
| dc.identifier.uri | http://kops.uni-konstanz.de/handle/123456789/15642 | |
| dc.language.iso | eng | deu |
| dc.legacy.dateIssued | 2011-11-09 | deu |
| dc.rights | terms-of-use | deu |
| dc.rights.uri | https://rightsstatements.org/page/InC/1.0/ | deu |
| dc.subject | noncommutative polynomials | deu |
| dc.subject | Nichtnegativstellensatz | deu |
| dc.subject | sums of squares | deu |
| dc.subject | semialgebraic sets | deu |
| dc.subject | contractive operators. | deu |
| dc.subject.ddc | 510 | deu |
| dc.title | A Nichtnegativstellensatz for polynomials in noncommuting variables | eng |
| dc.type | JOURNAL_ARTICLE | deu |
| dspace.entity.type | Publication | |
| kops.citation.bibtex | @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}
} | |
| kops.citation.iso690 | 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/s11856-007-0070-2 | deu |
| kops.citation.iso690 | 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/s11856-007-0070-2 | eng |
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| kops.identifier.nbn | urn:nbn:de:bsz:352-156429 | deu |
| kops.sourcefield | Israel Journal of Mathematics. 2007, <b>161</b>(1), pp. 17-27. ISSN 0021-2172. Available under: doi: 10.1007/s11856-007-0070-2 | deu |
| kops.sourcefield.plain | Israel Journal of Mathematics. 2007, 161(1), pp. 17-27. ISSN 0021-2172. Available under: doi: 10.1007/s11856-007-0070-2 | deu |
| kops.sourcefield.plain | Israel Journal of Mathematics. 2007, 161(1), pp. 17-27. ISSN 0021-2172. Available under: doi: 10.1007/s11856-007-0070-2 | eng |
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