  Let $U$ be a unitary operator defined on some infinite-dimensional complex
Hilbert space ${\cal H}$. Under some suitable regularity assumptions, it is
known that a local positive commutation relation between $U$ and an auxiliary
self-adjoint operator $A$ defined on ${\cal H}$ allows to prove that the
spectrum of $U$ has no singular continuous spectrum and a finite point
spectrum, at least locally. We show that these conclusions still hold under
weak regularity hypotheses and without any gap condition. As an application, we
study the spectral properties of the Floquet operator associated to some
perturbations of the quantum harmonic oscillator under resonant AC-Stark
potential.
