Connes' embedding conjectures and sums of hermitian squares


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KLEP, Igor, Markus SCHWEIGHOFER, 2008. Connes' embedding conjectures and sums of hermitian squares. In: Advances in Mathematics. 217(4), pp. 1816-1837. ISSN 0001-8708. Available under: doi: 10.1016/j.aim.2007.09.016

@article{Klep2008Conne-15621, title={Connes' embedding conjectures and sums of hermitian squares}, year={2008}, doi={10.1016/j.aim.2007.09.016}, number={4}, volume={217}, issn={0001-8708}, journal={Advances in Mathematics}, pages={1816--1837}, author={Klep, Igor and Schweighofer, Markus} }

2011-10-31T08:44:23Z Schweighofer, Markus 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 II<sub>1</sub>-factors are considered instead of matrices. Under the presence of Connes' conjecture, we derive degree bounds for the certificates. 2008 deposit-license eng Klep, Igor Schweighofer, Markus First publ. in: Advances in Mathematics 217 (2008), 4. - S. 1816-1837 Klep, Igor Connes' embedding conjectures and sums of hermitian squares 2011-10-31T08:44:23Z

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