Uniqueness of extensions of homogeneous polynomials on c0-sum of Hilbert spaces

We study the uniqueness of norm-preserving extension of n-homogeneous polynomials on X, where X is a c₀-sum of Hilbert spaces. We show that there exists a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on X to X″, but this result fails for homogeneous polynomials of degree greater than 2.