Abstract

Let U be a unitary operator defined on a infinite-dimensional separable complex Hilbert space H. Assume there exists a self-adjoint operator A on H such thatU* A U - A ≥ c I + K for some positive constant c and compact operator K. Then, assuming the commutators U* A U - A and [A, U* A U] admit a bounded extension over H, 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. © 2006 Elsevier Inc. All rights reserved.