Every nonreflexive subspace of L_1[0,1] fails the fixed point property
Functional Analysis
2016-09-06 v1
Abstract
The main result of this paper is that every non-reflexive subspace of fails the fixed point property for closed, bounded, convex subsets of and nonexpansive (or contractive) mappings on . Combined with a theorem of Maurey we get that for subspaces of , is reflexive if and only if has the fixed point property. For general Banach spaces the question as to whether reflexivity implies the fixed point property and the converse question are both still open.
Cite
@article{arxiv.math/9302208,
title = {Every nonreflexive subspace of L_1[0,1] fails the fixed point property},
author = {Paddy N. Dowling and Christopher J. Lennard},
journal= {arXiv preprint arXiv:math/9302208},
year = {2016}
}