Matches in SemOpenAlex for { <https://semopenalex.org/work/W4280591744> ?p ?o ?g. }
Showing items 1 to 69 of
69
with 100 items per page.
- W4280591744 abstract "A noncommutative (nc) polynomial is called (globally) trace-positive if its evaluation at any tuple of operators in a tracial von Neumann algebra has nonnegative trace. Such polynomials emerge as trace inequalities in several matrix or operator variables, and are widespread in mathematics and physics. This paper delivers the first Positivstellensatz for global trace positivity of nc polynomials. Analogously to Hilbert's 17th problem in real algebraic geometry, trace-positive nc polynomials are shown to be weakly sums of hermitian squares and commutators of regular nc rational functions. In two variables, this result is strengthened further using a new sum-of-squares certificate with concrete univariate denominators for nonnegative bivariate polynomials. The trace positivity certificates in this paper are obtained by convex duality through solving the so-called unbounded tracial moment problem, which arises from noncommutative integration theory and free probability. Given a linear functional on nc polynomials, the tracial moment problem asks whether it is a joint distribution of integral operators affiliated with a tracial von Neumann algebra. A counterpart to Haviland's theorem on solvability of the tracial moment problem is established. Moreover, a variant of Carleman's condition is shown to guarantee the existence of a solution to the tracial moment problem. Together with semidefinite optimization, this is then used to prove that every trace-positive nc polynomial admits an explicit approximation in the 1-norm on its coefficients by sums of hermitian squares and commutators of nc polynomials." @default.
- W4280591744 created "2022-05-22" @default.
- W4280591744 creator A5030756275 @default.
- W4280591744 creator A5031325549 @default.
- W4280591744 creator A5065891534 @default.
- W4280591744 date "2022-05-12" @default.
- W4280591744 modified "2023-09-27" @default.
- W4280591744 title "Globally trace-positive noncommutative polynomials and the unbounded tracial moment problem" @default.
- W4280591744 doi "https://doi.org/10.48550/arxiv.2205.05959" @default.
- W4280591744 hasPublicationYear "2022" @default.
- W4280591744 type Work @default.
- W4280591744 citedByCount "0" @default.
- W4280591744 crossrefType "posted-content" @default.
- W4280591744 hasAuthorship W4280591744A5030756275 @default.
- W4280591744 hasAuthorship W4280591744A5031325549 @default.
- W4280591744 hasAuthorship W4280591744A5065891534 @default.
- W4280591744 hasBestOaLocation W42805917441 @default.
- W4280591744 hasConcept C105795698 @default.
- W4280591744 hasConcept C114614502 @default.
- W4280591744 hasConcept C118615104 @default.
- W4280591744 hasConcept C121332964 @default.
- W4280591744 hasConcept C134306372 @default.
- W4280591744 hasConcept C138885662 @default.
- W4280591744 hasConcept C158693339 @default.
- W4280591744 hasConcept C202444582 @default.
- W4280591744 hasConcept C33923547 @default.
- W4280591744 hasConcept C41895202 @default.
- W4280591744 hasConcept C4285052 @default.
- W4280591744 hasConcept C49712288 @default.
- W4280591744 hasConcept C62520636 @default.
- W4280591744 hasConcept C68797384 @default.
- W4280591744 hasConcept C75291252 @default.
- W4280591744 hasConcept C90119067 @default.
- W4280591744 hasConcept C94940 @default.
- W4280591744 hasConcept C9679016 @default.
- W4280591744 hasConceptScore W4280591744C105795698 @default.
- W4280591744 hasConceptScore W4280591744C114614502 @default.
- W4280591744 hasConceptScore W4280591744C118615104 @default.
- W4280591744 hasConceptScore W4280591744C121332964 @default.
- W4280591744 hasConceptScore W4280591744C134306372 @default.
- W4280591744 hasConceptScore W4280591744C138885662 @default.
- W4280591744 hasConceptScore W4280591744C158693339 @default.
- W4280591744 hasConceptScore W4280591744C202444582 @default.
- W4280591744 hasConceptScore W4280591744C33923547 @default.
- W4280591744 hasConceptScore W4280591744C41895202 @default.
- W4280591744 hasConceptScore W4280591744C4285052 @default.
- W4280591744 hasConceptScore W4280591744C49712288 @default.
- W4280591744 hasConceptScore W4280591744C62520636 @default.
- W4280591744 hasConceptScore W4280591744C68797384 @default.
- W4280591744 hasConceptScore W4280591744C75291252 @default.
- W4280591744 hasConceptScore W4280591744C90119067 @default.
- W4280591744 hasConceptScore W4280591744C94940 @default.
- W4280591744 hasConceptScore W4280591744C9679016 @default.
- W4280591744 hasLocation W42805917441 @default.
- W4280591744 hasOpenAccess W4280591744 @default.
- W4280591744 hasPrimaryLocation W42805917441 @default.
- W4280591744 hasRelatedWork W162612020 @default.
- W4280591744 hasRelatedWork W2033532497 @default.
- W4280591744 hasRelatedWork W2057997389 @default.
- W4280591744 hasRelatedWork W2121030460 @default.
- W4280591744 hasRelatedWork W2326718950 @default.
- W4280591744 hasRelatedWork W2331735732 @default.
- W4280591744 hasRelatedWork W2950111834 @default.
- W4280591744 hasRelatedWork W3138834518 @default.
- W4280591744 hasRelatedWork W4280591744 @default.
- W4280591744 hasRelatedWork W4306795895 @default.
- W4280591744 isParatext "false" @default.
- W4280591744 isRetracted "false" @default.
- W4280591744 workType "article" @default.