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A noncommutative moment problem


Author: Don Hadwin
Journal: Proc. Amer. Math. Soc. 129 (2001), 1785-1791
MSC (2000): Primary 44A60, 46L89; Secondary 46L50, 47A57
DOI: https://doi.org/10.1090/S0002-9939-01-05772-0
Published electronically: January 23, 2001
MathSciNet review: 1814111
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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 ${II}_1$ 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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Additional Information

Don Hadwin
Affiliation: Department of Mathematics, University of New Hampshire, Durham, New Hampshire 03824
Email: don@math.unh.edu

DOI: https://doi.org/10.1090/S0002-9939-01-05772-0
Keywords: Moments, tracial states, ${C}^*$-algebra, ultrapower, free product
Received by editor(s): June 2, 1999
Received by editor(s) in revised form: October 11, 1999
Published electronically: January 23, 2001
Dedicated: Dedicated to the memory of my brother, Gary, whose cheerful spirit still fills my heart
Communicated by: David R. Larson
Article copyright: © Copyright 2001 American Mathematical Society

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