A non-commutative, analytic version of Hilbert's 17-th problem in type II$_1$ von Neumann algebras
Operator Algebras
2007-05-23 v4
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.
Cite
@article{arxiv.math/0404458,
title = {A non-commutative, analytic version of Hilbert's 17-th problem in type II$_1$ von Neumann algebras},
author = {Florin Radulescu},
journal= {arXiv preprint arXiv:math/0404458},
year = {2007}
}
Comments
Some minor misprints were corrected