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 the C*-algebra of quasilocal observables of a free massless spinor field. We construct explicitly such representations in the case of II_{\infty} and III_λ factors, 0 < λ < 1.