  In a recent paper, Trifonov suggested a possible explicit model of a
PT-symmetric system based on a modification of the canonical commutation
relation. Although being rather intriguing, in his treatment many mathematical
aspects of the model have just been neglected, making most of the results of
that paper purely formal. For this reason we are re-considering the same model
and we repeat and extend the same construction paying particular attention to
all the subtle mathematical points. From our analysis the crucial role of Riesz
bases clearly emerges. We also consider coherent states associated to the
model.
