  In this paper, we mainly study the scattering operators for the
Poincar\'{e}-Einstein manifolds. Those operators give the fractional GJMS
operators $P_{2\gamma}$ for the conformal infinity. If a Poincar\'{e}-Einstein
manifolds $(X^{n+1}, g_+)$ is locally conformally flat and there exists an
representative $g$ for the conformal infinity $(M, [g])$ such that the scalar
curvature $R$ is a positive constant and $Q_4>0$, then we prove that
$P_{2\gamma}$ is positive for $\gamma\in (1,2)$ and thus the first real
scattering pole is less than $\frac{n}{2}-2$.
