Corpus ID: 2989301

A non-commutative, analytic version of Hilbert's 17-th problem in type II$_1$ von Neumann algebras

  title={A non-commutative, analytic version of Hilbert's 17-th problem in type II\$\_1\$ von Neumann algebras},
  author={Florin Radulescu},
  journal={arXiv: Operator Algebras},
  • F. Radulescu
  • Published 26 April 2004
  • Mathematics
  • arXiv: Operator Algebras
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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