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James quasi reflexive space has the fixed point property. (English) Zbl 0672.47045
Using the works of Maurey and Lin, the author proves that the classical sequence James space J has the fixed point property. The main result states:
Every weakly compact convex subset of J has the fixed point property.
This gives rise to an example of a Banach space with a non-unconditional basis.
Reviewer: Shaligram Singh

##### MSC:
 47H10 Fixed-point theorems 46B25 Classical Banach spaces in the general theory 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.
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##### References:
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