Every nonreflexive subspace of $L_1[0,1]$ fails the fixed point property
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- by P. N. Dowling and C. J. Lennard
- Proc. Amer. Math. Soc. 125 (1997), 443-446
- DOI: https://doi.org/10.1090/S0002-9939-97-03577-6
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Abstract:
The main result of this paper is that every nonreflexive subspace $Y$ of $L_{1}[0,1]$ fails the fixed point property for closed, bounded, convex subsets $C$ of $Y$ and nonexpansive (or contractive) mappings on $C$. Combined with a theorem of Maurey we get that for subspaces $Y$ of $L_{1}[0,1]$, $Y$ is reflexive if and only if $Y$ 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.References
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Bibliographic Information
- P. N. Dowling
- Affiliation: Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056
- C. J. Lennard
- Affiliation: Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
- Received by editor(s): March 25, 1995
- Received by editor(s) in revised form: August 4, 1995
- Communicated by: Dale Alspach
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 443-446
- MSC (1991): Primary 47H10
- DOI: https://doi.org/10.1090/S0002-9939-97-03577-6
- MathSciNet review: 1350940