Involve: A Journal of Mathematics
- Volume 4, Number 1 (2011), 65-74.
A note on moments in finite von Neumann algebras
By a result of the second author, the Connes embedding conjecture (CEC) is false if and only if there exists a self-adjoint noncommutative polynomial in the universal unital -algebra and positive, invertible contractions in a finite von Neumann algebra with trace such that and for every positive integer and all positive definite contractions in . We prove that if the real parts of all coefficients but the constant coefficient of a self-adjoint polynomial have the same sign, then such a cannot disprove CEC if the degree of is less than , and that if at least two of these signs differ, the degree of is , the coefficient of one of the is nonnegative and the real part of the coefficient of is zero then such a disproves CEC only if either the coefficient of the corresponding linear term is nonnegative or both of the coefficients of and are negative.
Involve, Volume 4, Number 1 (2011), 65-74.
Received: 9 July 2010
Accepted: 26 February 2011
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46L10: General theory of von Neumann algebras
Secondary: 46L54: Free probability and free operator algebras
Bannon, Jon; Hadwin, Donald; Jeffery, Maureen. A note on moments in finite von Neumann algebras. Involve 4 (2011), no. 1, 65--74. doi:10.2140/involve.2011.4.65. https://projecteuclid.org/euclid.involve/1513733363