Abstract
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.
Citation
Jon Bannon. Donald Hadwin. Maureen Jeffery. "A note on moments in finite von Neumann algebras." Involve 4 (1) 65 - 74, 2011. https://doi.org/10.2140/involve.2011.4.65
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