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A non-commutative, analytic version of Hilbert's 17-th problem in type II1 von Neumann algebras

2004/04/26 by Florin Radulescu, Radulescu, Florin
Mathematics · #46L10 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L10

paper · pdf · doi:10.48550/arxiv.math/0404458

Some minor misprints were corrected

arxiv created 2005/02/12 · arxiv updated 2009/12/01

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.

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