Dominated polynomials on $\mathcal{L}_P $ -spaces

It is well known that continuous bilinear forms on C(K) × C(K) are 2-dominated. This paper shows that generalizations of this result are not to be expected. The main result asserts that for every -space E(1 p ), every n 2, every r > 0 and every Banach space F , there exists an n-homogeneous polynomial P : E F such that P is not of type _r], hence P is neither r-dominated nor r-semi-integral (if n = 2 and p = , F is supposed to contain an isomorphic copy of some , 1_q < ).Received: 24 November 2003