  If frequent measurements ascertain whether a quantum system is still in a
given subspace, it remains in that subspace and a quantum Zeno effect takes
place. The limiting time evolution within the projected subspace is called
quantum Zeno dynamics. This phenomenon is related to the limit of a product
formula obtained by intertwining the time evolution group with an orthogonal
projection.
  By introducing a novel product formula we will give a characterization of the
quantum Zeno effect for finite-rank projections, in terms of a spectral decay
property of the Hamiltonian in the range of the projections. Moreover, we will
also characterize its limiting quantum Zeno dynamics and exhibit its (not
necessarily lower-bounded) generator as a generalized mean value Hamiltonian.
