Factorization of operator-valued polynomials in several non-commuting variables☆

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Matrix-J-unitary Non-commutative Rational Formal Power Series (2004, unknown): “, matrix-positivity of non-commutative polynomials (non-commutative Positivstellensatz) [29, 40, 31, 32], matrix-positivity of FPS kernels [34], matrix-convexity [21, 30].”
On Factorization of Trigonometric Polynomials (2004, result): “Related results have been obtained by Scott McCullough [ 10 ], who has shown that factorizations always exist for trigonometric polynomials in noncommuting variables.”
About the Connes Embedding Conjecture---Algebraic approaches--- (2012, methodology): “lows that the entry X s,t of the positive matrix X∈ ME′(B) depends only on s−1tand Xis of the form (ρE′ ⊗ idB)(g′). The following is slightly more precise than Theorem 7.1 in [BT] (and Theorem 0.1 in [Mc]). It implies B(H)⊗max k [Fd] = B(H)⊗min [Fd], and hence Theorem 20. Theorem 25 ([BT]). Let B= B”
Noncommutative sums of squares (2005, background): “The approach here can also be adapted to deal with the case of self-adjoint variables where x∗j = x j [McCullough 2001].”