  We give examples of composition operators $C\_\Phi$ on $H^2 (\D^2)$ showing
that the condition $\|\Phi \|\_\infty = 1$ is not sufficient for their
approximation numbers $a\_n (C\_\Phi)$ to satisfy $\lim\_{n \to \infty} [a\_n
(C\_\Phi) ]^{1/\sqrt{n}} = 1$, contrary to the $1$-dimensional case. We also
give a situation where this implication holds. We make a link with the
Monge-Amp\`ere capacity of the image of $\Phi$.
