  In a recent series of papers we have analyzed a certain deformation of the
canonical commutation relations producing an interesting functional structure
which has been proved to have some connections with physics, and in particular
with quasi-hermitian quantum mechanics. Here we repeat a similar analysis
starting with the canonical anticommutation relations. We will show that in
this case most of the assumptions needed in the former situation are
automatically satisfied, making our construction rather {\em friendly}. We
discuss some examples of our construction, again related to quasi-hermitian
quantum mechanics, and the bi-coherent states for the system.
