  We present a new proof of a Sundaresan's result which shows that the space of
orthogonally additive polynomials $\mathcal{P}_o(^k\ell_p)$ is isometrically
isomorphic to $\ell_{p/p-k}$ if $k<p<\infty$ and to $\ell_\infty$ if $1\leq
p\leq k$.
