Matrix tests yield a support-function characterization of the tau-closed C*-convex hull of families of completely positive maps between operator systems and C*-algebras.
Kriel,An introduction to matrix convex sets and free spectrahedra, Complex Anal
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Matrix-Test Duality: A Support-Function Characterization for $C^*$-Convex Families of CP Maps
Matrix tests yield a support-function characterization of the tau-closed C*-convex hull of families of completely positive maps between operator systems and C*-algebras.