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Effective non-Hermitian Hamiltonians describing decaying systems are derivedand analyzed in connection with the occurrence of possible Hilbert spacepartitioning, resulting in a confinement of the dynamics. In some cases, thisfact can be interpreted properly as Zeno effect or Zeno dynamics, according tothe dimension of the subspace one focuses on; in some other cases, theinterpretation is more complicated and traceable back to a mix of Zenophenomena and lack of resonance. Depending on the complex phases of thediagonal terms of the Hamiltonian, the system reacts in different ways,requiring larger moduli for the dynamical confinement to occur when the complexphase is close to $\pi/2$.

Hilbert space partitioning for non-Hermitian Hamiltonians: From off-resonance to Zeno subspaces