On the Representation of Orthogonally Additive Polynomials in ${\ell }_p$

Abstract

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 $1\le p\le k$.