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

Published online by Cambridge University Press:  24 October 2008

Gilles Pisier
Affiliation:
Texas A. andM. University and Equipe D'Analyse, Université; ParisVI, Tour 46 –4ème Etage, 4, Place Jussieu, 75252 –; ParisCedex 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

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

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1988

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