  We show that if $M$ is a compact oriented surface of genus 0 and $G$ is a
subgroup of $\Symp^\omega_\mu(M)$ which has an infinite normal solvable
subgroup, then $G$ is virtually abelian. In particular the centralizer of an
infinite order $f \in \Symp^\omega_\mu(M)$ is virtually abelian. Another
immediate corollary is that if $G$ is a solvable subgroup of
$\Symp^\omega_\mu(M)$ then $G$ is virtually abelian. We also prove a special
case of the Tits Alternative for subgroups of $\Symp^\omega_\mu(S^2).$
