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The normal structure of James quasi reflexive space. (English) Zbl 0724.46014
A nonempty bounded convex subset K of a Banach space X has normal structure if for every convex subset H of K with \(diam(H)>0\), there is z in H such that \(diam(H)>\sup \{\| x-z\|:\;x\in H\}.\) The interest of this concept comes from the fact that weakly compact convex sets with normal structure have the fixed point property for nonexpansive mappings. In this paper it is proved that weakly compact convex subsets of James space J have normal structure.

46B04 Isometric theory of Banach spaces
46B20 Geometry and structure of normed linear spaces
47H10 Fixed-point theorems
46B25 Classical Banach spaces in the general theory
Full Text: DOI
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