  We consider the special type of pseudo-bosonic systems that can be mapped to
standard bosons by means of generalized Bogoliubov transformation and
demonstrate that a pseudo-Hermitian systems can be obtained from them by means
of a second subsequent Bogoliubov transformation. We employ these operators in
a simple model and study three different types of scenarios for the constraints
on the model parameters giving rise to a Hermitian system, a pseudo-Hermitian
system in which the second the Bogoliubov transformations is equivalent to the
associated Dyson map and one in which we obtain D-quasi bases.
