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

Abstract

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

S0305004100064902_eqn001

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)