Some classes of multilinear operators on C(K) spaces

We obtain a classification of projective tensor products of C(K) spaces according to whether none, exactly one or more than one factor contains copies of 1, in terms of the behaviour of certain classes of multilinear operators on the product of the spaces or the verification of certain Banach space properties of the corresponding tensor product. The main tool is an improvement of some results of Emmanuele and Hensgen on the reciprocal Dunford-Pettis and Pelczynski's (V) properties of the projective tensor product of Banach spaces. We also study relationships between several classes of multilinear operators and the associated linear operators.