  In this paper we investigate the dynamics of the quantum Zeno subspaces which
are the eigenspaces of the interaction Hamiltonian, belonging to different
eigenvalues. Using the perturbation theory and the adiabatic approximation, we
get a general expression of the jump probability between different Zeno
subspaces. We applied this result in some examples. In these examples, as the
coupling constant of the interactions increases, the measurement keeps the
system remaining in its initial subspace and the quantum Zeno effect takes
place.
