Connes' embedding conjecture and sums of hermitian squares

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dc.contributor.author Klep, Igor en
dc.contributor.author Schweighofer, M en
dc.date.accessioned 2012-05-22T22:57:55Z en
dc.date.issued 2008 en
dc.identifier.citation Advances in Mathematics 217(4):1816-1837 2008 en
dc.identifier.issn 0001-8708 en
dc.identifier.uri http://hdl.handle.net/2292/18130 en
dc.description.abstract We show that Connes' embedding conjecture on von Neumann algebras is equivalent to the existence of certain algebraic certificates for a polynomial in noncommuting variables to satisfy the following nonnegativity condition: The trace is nonnegative whenever self-adjoint contraction matrices of the same size are substituted for the variables. These algebraic certificates involve sums of hermitian squares and commutators. We prove that they always exist for a similar nonnegativity condition where elements of separable II1-factors are considered instead of matrices. Under the presence of Connes' conjecture, we derive degree bounds for the certificates. en
dc.publisher Elsevier en
dc.relation.ispartofseries Advances in Mathematics en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from http://www.sherpa.ac.uk/romeo/issn/0001-8708/ en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.title Connes' embedding conjecture and sums of hermitian squares en
dc.type Journal Article en
dc.identifier.doi 10.1016/j.aim.2007.09.016 en
pubs.issue 4 en
pubs.begin-page 1816 en
pubs.volume 217 en
dc.rights.holder Copyright: Elsevier en
pubs.end-page 1837 en
dc.rights.accessrights http://purl.org/eprint/accessRights/RestrictedAccess en
pubs.subtype Article en
pubs.elements-id 243207 en
pubs.arxiv-id math/0607615 en
dc.identifier.eissn 1090-2082 en
pubs.record-created-at-source-date 2012-05-23 en


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