An operator-valued Positivstellensatz equates positivity on matrix convex sets to a weighted sum-of-squares form, enabling an explicit sum-of-squares factorization for positive trigonometric polynomials on free products of finite abelian groups.
Davidson, Adam Dor-On, Orr Moshe Shalit, Baruch Solel, Dilations, Inclusions of Matrix Convex Sets, and Completely Positive Maps , Int
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Operator-Valued Positivstellens\"atze on Matrix Convex Sets and Free Products of Finite Abelian Groups
An operator-valued Positivstellensatz equates positivity on matrix convex sets to a weighted sum-of-squares form, enabling an explicit sum-of-squares factorization for positive trigonometric polynomials on free products of finite abelian groups.