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Parallels between the notions of nonlinear pseudobosons and of an apparentnon-Hermiticity of observables as shown in paper I (arXiv: 1109.0605) aredemonstrated to survive the transition to the quantum models based on the useof unbounded metric in the Hilbert space of states.

Non linear pseudo-bosons versus hidden Hermiticity. II: The case of unbounded operators