  For the reference triangle or tetrahedron $T$, we study the stability
properties of the $L^2(T)$-projection $\Pi_N$ onto the space of polynomials of
degree $N$. We show $\|\Pi_N u\|_{L^2(\partial T)}^2 \leq C \|u\|_{L^2(T)}
\|u\|_{H^1(T)}$. This implies optimal convergence rates for the approximation
error $\|u - \Pi_N u\|_{L^2(\partial T)}$ for all $u \in H^k(T)$, $k > 1/2$.
