Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The dual J* of the James space has cotype 2 and the Gordon-Lewis property

Gilles Pisiera1

a1 Texas A. and M. University and Equipe D'Analyse, Université; Paris VI, Tour 46 –4ème Etage, 4, Place Jussieu, 75252 –; Paris Cedex 05


We prove the result in the title. More generally we consider the Banach space υp, of all sequences (xn) of scalars such that


where the supremum runs over all increasing sequences n1n2 ≤ …. We show that S0305004100064902_inline001 is of cotype 2 if p xs227D 2 and of cotype p′, where 1/p′ + 1/p = 1, if p ≤ 2. Similar results are obtained for the analogous function spaces.

(Received May 25 1987)