Function spaces not containing l1

For Omega bounded and open subset of R(d)0 and X a reflexive Banach space with 1-symmetric basis, the function space JF(X) (Omega) is defined. This class of spaces includes the classical James function space. Every member of this class is separable and has non-separable dual. We provide a proof of topological nature that JF(X)(Omega) does not contain an isomorphic copy of l(1). We also investigate the structure of these spaces and their duals.