This is an announcement for the paper "A new proof of James' sup theorem" by Marianne Morillon.

Abstract: We provide a new proof of James' sup theorem for (non necessarily separable) Banach spaces. One of the ingredients is the following generalization of a theorem of Hagler and Johnson (1977) : "If a normed space $E$ does not contain any asymptotically isometric copy of $\ell^1(\IN)$, then every bounded sequence of $E'$ has a normalized block sequence pointwise converging to $0$".

Archive classification: Functional Analysis

Mathematics Subject Classification: 46B ; 03E25

Report Number: ERMIT-MM-07jan2005

The source file(s), envoi.bbl: 2807 bytes, envoi.tex: 35905 bytes, icone-ermit.eps: 24310 bytes, is(are) stored in gzipped form as 0505176.tar.gz with size 19kb. The corresponding postcript file has gzipped size 69kb.

Submitted from: Marianne.Morillon@univ-reunion.fr

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http://arXiv.org/abs/math.FA/0505176

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