  For a smooth projective unitary representation of a locally convex Lie group
G, the projective space of smooth vectors is a locally convex Kaehler manifold.
We show that the action of G on this space is weakly Hamiltonian, and lifts to
a Hamiltonian action of the central U(1)-extension of G obtained from the
projective representation. We identify the non-equivariance cocycles obtained
from the weakly Hamiltonian action with those obtained from the projective
representation, and give some integrality conditions on the image of the
momentum map.
