Trace-positive polynomials and the quartic tracial moment problem

DOI10.1016/j.crma.2010.06.005zbMath1205.15047OpenAlexW2082001098MaRDI QIDQ990194

Igor Klep, Sabine Burgdorf

Publication date: 6 September 2010

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-119770

zbMATH Keywords

cyclic equivalencesum of hermitian squarestrace-positive polynomialtracial moment problem

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Positive matrices and their generalizations; cones of matrices (15B48) Miscellaneous inequalities involving matrices (15A45) Classifications of (C^*)-algebras (46L35) Rings with polynomial identity (16R99) Real algebra (13J30)

Related Items (9)

The strong truncated Hamburger moment problem with and without gaps ⋮ Dimensional stability in truncated moment problems ⋮ The singular bivariate quartic tracial moment problem ⋮ Real zero polynomials and A. Horn's problem ⋮ The tracial moment problem on quadratic varieties ⋮ The truncated Hamburger moment problems with gaps in the index set ⋮ NONNEGATIVE POLYNOMIALS, SUMS OF SQUARES AND THE MOMENT PROBLEM ⋮ trace-positive non-commutative polynomials ⋮ On matrix algebras associated to sum-of-squares semidefinite programs

Cites Work

• Positivity of Riesz functionals and solutions of quadratic and quartic moment problems
• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• Extremal positive semidefinite forms
• A new approach to Hilbert's theorem on ternary quartics
• ``Positive noncommutative polynomials are sums of squares.
• Connes' embedding conjecture and sums of Hermitian squares
• The truncated tracial moment problem
• Solution of the truncated complex moment problem for flat data
• The proof of Tchakaloff’s Theorem
• Factorization of operator-valued polynomials in several non-commuting variables
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