The core of this paper lies in several observations centered around
the decomposition of the unit operator for a certain generalized
Landau level model and, secondly, for a damped harmonic oscillator.
By their structure, both models are shown to fit in the general
scheme based on the bosonic creation and annihilation operators
acting in a biorthogonal-basis arrangement (called, by one of the
authors, pseudobosonic) but one reveals that certain assumptions
(making the theory simpler) appear violated. Some consequences are
outlined and discussed, and future work on the problem is promised.

MR2779604 Ali, S. Twareque; Bagarello, F.; Gazeau, Jean Pierre
Modified Landau levels, damped harmonic oscillator, and
two-dimensional pseudo-bosons. J. Math. Phys. 51 (2010), no. 12,
123502, 11 pp. 81Qxx