Reflexivity and the Fixed-Point Property for Nonexpansive Maps |
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Authors: | PN Dowling CJ Lennard B Turett |
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Institution: | aMiami University, Oxford, Ohio, 45056;bUniversity of Pittsburgh, Pittsburgh, Pennsylvania, 15260;cOakland University, Rochester, Michigan, 48309;dUniversity College, Galway, Ireland |
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Abstract: | Connections between reflexivity and the fixed-point property for nonexpansive self-mappings of nonempty, closed, bounded, convex subsets of a Banach space are investigated. In particular, it is shown thatl1(Γ) for uncountable sets Γ andl∞cannot even be renormed to have the fixed-point property. As a consequence, if an Orlicz space on a finite measure space that is not purely atomic is endowed with the Orlicz norm, the Orlicz space has the fixed-point property exactly when it is reflexive. |
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