Representations obeying the spectrum condition

We show that every properly infinite, injective von Neumann algebra acting on a separable Hilbert space is isomorphic to the weak closure of some translation covariant representation, obeying the spectrum condition for the generators of the translation group, of theC*-algebra of quasilocal observables of a free massless spinor field. We construct explicitly such representations in the case ofII andIII factors, 0<<1.