Quantization of $A_{0}(K)$-Spaces (1802.03481v1)

Abstract: In this paper, we study $L^1$-matrix convex sets ${K_{n}}$ in $$-locally convex spaces and show that every C$^$-ordered operator space is complete isometrically, completely isomorphic to ${A_{0}(K_{n}, M_{n}(V))}$ for a suitable $L^1$-matrix convex set ${K_{n}}$. Further, we generalize the notion of regular embedding of a compact convex set to $L^{1}$-regular embedding of $L^{1}$-matrix convex set. Using $L^{1}$-regular embedding of $L^{1}$-convex set, we find conditions under which $A_{0}(K_{n}, M_{n}(V))$ is an abstract operator system.