Orthogonally additive polynomials on spaces of continuous functions

We show that, for every orthogonally additive homogeneous polynomial P on a space of continuous functions C(K) with values in a Banach space Y , there exists a linear operator S : C(K)→Y such that P(f) = S(f n). This is the C(K) version of a related result of Sundaresam for polynomials on Lp spaces.  2004 Elsevier Inc. All rights reserved