We prove a non-commutative version of the Hilbert's 17th problem, giving a characterization of the class of non-commutative polynomials in n-undeterminates that have positive trace when evaluated in n-selfadjoint elements in arbitrary II1 von Neumann algebra. As a corollary we prove that Connes's embedding conjecture is equivalent to a statement that can be formulated entirely in the context of finite matrices.
Radulescu, F. (2008). A non-commutative, analytic version of Hilbert's 17th problem in type II1 von Neumann algebras. In F.R. Ken Dykema (a cura di), Von Neumann algebras in Sibiu (pp. 93-101). Bucharest : Theta.
A non-commutative, analytic version of Hilbert's 17th problem in type II1 von Neumann algebras
RADULESCU, FLORIN
2008-01-01
Abstract
We prove a non-commutative version of the Hilbert's 17th problem, giving a characterization of the class of non-commutative polynomials in n-undeterminates that have positive trace when evaluated in n-selfadjoint elements in arbitrary II1 von Neumann algebra. As a corollary we prove that Connes's embedding conjecture is equivalent to a statement that can be formulated entirely in the context of finite matrices.File in questo prodotto:
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