  We demonstrate new abstract characterizations for unital and non-unital
operator spaces. We characterize unital operator spaces in terms of the cone of
accretive operators (operators whose real part is positive). Defining the gauge
of an operator $T \in B(H)$ to be $\|Re(T)_+\|$, we demonstrate an abstract
characterization of operator spaces up to complete gauge-isometry. Both of
these characterizations preserve the structure of the self-adjoint, positive,
and accretive operators, as well as the operator norm. We show that an operator
space with a given matrix ordering of positive or accretive cones can be
represented completely isometrically and completely order isomorphically if and
only if each positive cone is normal, in the sense that $x \leq y \leq z$
implies that $\|y\| \leq \max(\|x\|,\|z\|)$ at each matrix level. This is
achieved by showing that normal matrix ordered operator spaces are induced by
gauges. We show that inducing gauges are not unique in general. Finally, we
show that completely positive completely contractive linear maps on non-unital
operator spaces extend to any containing operator system if and only if the
operator space is induced by a unique gauge.
