  Let D be a self-adjoint differential operator of Dirac type acting on
sections in a vector bundle over a closed Riemannian manifold M. Let H be a
closed D-invariant subspace of the Hilbert space of square integrable sections.
Suppose D restricted to H is semibounded. We show that every element u in H has
the weak unique continuation property, i.e. if u vanishes on a nonempty open
subset of M, then it vanishes on all of M.
