Dual spaces of operator systems

The aim of this article is to give an infinite dimensional analogue a result Choi and Effros concerning dual spaces finite unital operator systems. An (not necessarily unital) system self-adjoint subspace L(H), equipped with the induced matrix norm cone. We say that T dualizable if one can find equivalent on space T? such under canonical cone, becomes system. show only ordered normed M?(T)sa satisfies form bounded decomposition property. In case,?f?d:=sup?{?[fi,j(xk,l)]?:x?Mn(T)+;?x??1;n?N}(f?Mm(T?);m?N), largest dominated by original turns it into system, denoted Td. It be shown Td again dualizable. For every completely positive map ?:S?T between systems, there unique weak-?-continuous ?d:Td?Sd which compatible ??. From this, we obtain full faithful functor from category systems Moreover, will verify S either C?-algebra or then weak-?-homeomorphism S?? (Sd)d isometric complete order isomorphism. Furthermore, via duality above, C?-algebras (both contractions as their morphisms) regarded subcategories (with its morphisms). Consequently, nice framework for obtained, includes all