  Let M be a connected Riemannian manifold and let D be a Dirac type operator
acting on smooth compactly supported sections in a Hermitian vector bundle over
M. Suppose D has a self-adjoint extension A in the Hilbert space of
square-integrable sections. We show that any $L^2$-section $\phi$ contained in
a closed A-invariant subspace onto which the restriction of A is semi-bounded
has the unique continuation property: if $\phi$ vanishes on a non-empty open
subset of M, then it vanishes on all of M.
