Weak compactness and fixed point property for affine mappings

It is shown that a closed convex bounded subset of a Banach space is weakly compact if and only if it has the generic fixed point property for continuous affine mappings. The class of continuous affine mappings can be replaced by the class of affine mappings which are uniformly Lipschitzian with som...

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Bibliographic Details
Published in:Journal of functional analysis 2004-04, Vol.209 (1), p.1-15
Main Authors: Benavides, T.Domı́nguez, Pineda, M.A.Japón, Prus, S.
Format: Article
Language:English
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Summary:It is shown that a closed convex bounded subset of a Banach space is weakly compact if and only if it has the generic fixed point property for continuous affine mappings. The class of continuous affine mappings can be replaced by the class of affine mappings which are uniformly Lipschitzian with some constant M>1 in the case of c 0, the class of affine mappings which are uniformly Lipschitzian with some constant M> 6 in the case of quasi-reflexive James’ space J and the class of nonexpansive affine mappings in the case of L-embedded spaces.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2002.02.001