Non-self-adjoint hamiltonians defined by Riesz bases
  We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, {we give conditions under which these Hamiltonians} can be factorized in terms of generalized lowering and raising operators. 
F. Bagarello, A. Inoue, C. Trapani
math-ph math.MP quant-ph