Some classes of multilinear operators on C(k) spaces

Abstract

The authors obtain in this paper a classification of projective tensor products of C(K) spaces, 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 used is an improvement of some results of Emmanuele and Hensgen on the reciprocal Dunford-Pettis and Pełczy´nski’s (V) properties of the projective tensor product of Banach spaces. Finally, the paper ends with a study of the relationships between some classes of multilinear operators and their linearizations.