Non-commutative Caratheodory Interpolation

We prove a Caratheodory-Fejer type interpolation theorem for certain matrix convex sets in ${\text{C}}^d$ using the Blecher-Ruan-Sinclair characterization of abstract operator algebras. Our results generalize the work of Dmitry S. Kalyuzhnyi-Verbovetzkii for the d-dimensional non-commutative polydisc.