  We investigate the properties of the collision operator associated to the
linear Boltzmann equation for dissipative hard-spheres arising in granular gas
dynamics. We establish that, as in the case of non-dissipative interactions,
the gain collision operator is an integral operator whose kernel is made
explicit. One deduces from this result a complete picture of the spectrum of
the collision operator in an Hilbert space setting, generalizing results from
T. Carleman to granular gases. In the same way, we obtain from this integral
representation of the gain operator that the semigroup in $L^1(\R \times \R,\d
\x \otimes \d\v)$ associated to the linear Boltzmann equation for dissipative
hard spheres is honest generalizing known results from the first author.
