  We investigate some examples of quantum Zeno dynamics, when a system
undergoes very frequent (projective) measurements that ascertain whether it is
within a given spatial region. In agreement with previously obtained results,
the evolution is found to be unitary and the generator of the Zeno dynamics is
the Hamiltonian with hard-wall (Dirichlet) boundary conditions. By using a new
approach to this problem, this result is found to be valid in an arbitrary
$N$-dimensional compact domain. We then propose some preliminary ideas
concerning the algebra of observables in the projected region and finally look
at the case of a projection onto a lower dimensional space: in such a situation
the Zeno ansatz turns out to be a procedure to impose constraints.
