  The dynamical properties of a quantum system can be profoundly influenced by
its environment. Usually, the environment provokes decoherence and its action
on the system can often be schematized by adding a noise term in the
Hamiltonian. However, other scenarios are possible: we show that by increasing
the strength of the noise, the Hilbert space of the system gradually splits
into invariant subspaces, among which transitions become increasingly
difficult. The phenomenon is equivalent to the formation of the quantum Zeno
subspaces. We explore the possibility that noise can {\em prevent}, rather than
provoke decoherence.
