  We demonstrate that not all generalized Bogoliubov transformations lead to
$\cal D$-pseudo-bosons and prove that a correspondence between the two can only
be achieved with the imposition of specific constraints on the parameters
defining the transformation. For certain values of the parameters we find that
the norms of the vectors in sets of eigenvectors of two related apparently non
self-adjoint number-like operators possess different types of asymptotic
behavior. We use this result to deduce further that they constitute bases for a
Hilbert space, albeit neither of them can form a Riesz base. When the
constraints are relaxed they cease to be Hilbert space bases, but remain $\cal
D$-quasi bases.
