On the representation of orthogonally additive polynomials in ${\mathrm{\ell }}_p$

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