Function spaces not containing ℓ1

For Ω bounded and open subset of\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$B^{d_0 } $$ \end{document} andX a reflexive Banach space with 1-symmetric basis, the function spaceJFX(Ω) 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 thatJFX(Ω) does not contain an isomorphic copy of ℓ1. We also investigate the structure of these spaces and their duals.