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Structure des cones normaux contenus dans un espace de Banach ou son dual II

Published online by Cambridge University Press:  17 April 2009

Richard Becker
Richard Becker
Affiliation:
Equipe D'Analyse Unité associée au C.N.R.S. No 754 Tour 46, 4ièmie étage, Universite Paris VI, 4 Place Jussieu 75252 Paris Cedex 05, France
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Let B be a Banach space and X ⊂ B a normal cone such that the norm is monotone on X for the order determinated by X.

We study the sup, denoted by i(X), of the q ≥ 1 such that, for each E> 0 and each n, there are x1, …, xn in X such that:

for all a1, …, an ≥ 0, where ‖ ‖q is the norm in lq.

We prove that i(X) is the inf of the p for which we have:

The proof use a similar theorem of Kirvine, concerning Banach Riesz spaces. Here conical measures are a useful tool. We establish a link with a preceding work in which we adapt the Maurey theory factorisation of operators with values in a LP space, to the case of normal cones, contained in a Banach space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 3 , June 1993 , pp. 427 - 434
Copyright
Copyright © Australian Mathematical Society 1993

References

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