Floquet operators without singular continuous spectrum

Let U   be a unitary operator defined on a infinite-dimensional separable complex Hilbert space HH. Assume there exists a self-adjoint operator A   on HH such thatU∗AU−A⩾cI+KU∗AU−A⩾cI+K for some positive constant c and compact operator K  . Then, assuming the commutators U∗AU−AU∗AU−A and [A,U∗AU][A,U∗AU] admit a bounded extension over HH, we prove the spectrum of the operator U has no singular continuous component and only a finite number of eigenvalues of finite multiplicity. We give a localized version of this result and apply it to study the spectrum of the Floquet operator of periodic time-dependent kicked quantum systems.