  We characterize weak* closed unital vector spaces of operators on a Hilbert
space $H$. More precisely, we first show that an operator system, which is the
dual of an operator space, can be represented completely isometrically and
weak* homeomorphically as a weak* closed operator subsystem of $B(H)$. An
analogous result is proved for unital operator spaces. Finally, we give some
somewhat surprising examples of dual unital operator spaces.
