  We show that, on any asymptotically hyperbolic surface, the essential
spectrum of the Lichnerowicz Laplacian $\Delta_L$ contains the ray
$[{1/4},+\infty[$. If moreover the scalar curvature is constant then -2 and 0
are infinite dimensional eigenvalues. If, in addition, the inequality $<\Delta
u, u>_{L^2}\geq \frac14||u||^2_{L^2}$ holds for all smooth compactly supported
function $u$, then there is no other value in the spectrum.
