A noncommutative moment problem

Hadwin, Don

doi:10.1090/S0002-9939-01-05772-0

A noncommutative moment problem
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Proc. Amer. Math. Soc. 129 (2001), 1785-1791 Request permission

Abstract:

We prove a noncommutative moment theorem and relate it to Connes’ problem of embedding finite factor von Neumann algebras into an ultraproduct of the hyperfinite $\mathrm {II}_1$ factor. We include a linear-algebraic equivalent of Connes’ problem, which asks for a characterization of all noncommutative polynomials which have positive trace when the variables are replaced by contractive hermitian $n\times n$ matrices.

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