  A theorem of Davis, Figiel, Johnson and Pe{\l}czy\'nski tells us that
weakly-compact operators between Banach spaces factor through reflexive Banach
spaces. The machinery underlying this result is that of the real interpolation
method, which has been adapted to the category of operator spaces by Xu,
showing the this factorisation result also holds for completely bounded
weakly-compact maps. In this note, we show that Xu's ideas can be adapted to
give an intrinsic characterisation of when a completely contractive Banach
algebra arises as a closed subalgebra of the algebra of completely bounded
operators on a reflexive operator space. This result was shown by Young for
Banach algebras, and our characterisation is a direct analogue of Young's,
involving weakly almost periodic functionals.
