We define and describe the class of Quasi-Töplitz
functions. We then prove an abstract KAM theorem where the
perturbation is in this class. We apply this theorem to a
nonlinear Schrödinger equation (NLS) on the torus Td, thus proving
existence and stability of quasi-periodic solutions and recovering
the results of Eliasson and Kuksin. With respect to that paper
consider only the NLS which preserves the total momentum and exploit
this conserved quantity in order to simplify our treatment.