Function spaces not containing ℓ1Function spaces not containing ℓ1 Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-11-142003enFor Ω bounded and open subset ofBd0 andX a reflexive Banach space with 1-symmetric basis, the function spaceJF X (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 thatJF X (Ω) does not contain an isomorphic copy of ℓ1. We also investigate the structure of these spaces and their duals.http://creativecommons.org/licenses/by/4.0/Israel Journal of Mathematics113529-81 Manousakis Antonios Μανουσακης Αντωνιος Petrakis, Marina Deliyanni,I Springer Verlag