  In this paper we consider some aspects of tridiagonal, non self-adjoint,
Hamiltonians and of their supersymmetric counterparts. In particular, the
problem of factorization is discussed, and it is shown how the analysis of the
eigenstates of these Hamiltonians produce interesting recursion formulas giving
rise to biorthogonal families of vectors. Some examples are proposed, and a
connection with bi-squeezed states is analyzed.
