Reflexivity is equivalent to stability of the almost fixed point property
In this work we show that the family of closed convex sets with the almost fixed point property is not stable under renormings for non-reflexive Banach spaces. This, together with a result by Reich, shows that a Banach space is reflexive if and only if it has the same family of closed convex sets wi...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/182208 |
| Acceso en línea: | https://hdl.handle.net/11441/182208 https://doi.org/10.1016/j.jmaa.2017.11.007 |
| Access Level: | acceso abierto |
| Palabra clave: | Reflexive Banach spaces Equivalent norms Nonexpansive mappings Almost fixed point property AFPP Stability Directionally bounded sets |
| Sumario: | In this work we show that the family of closed convex sets with the almost fixed point property is not stable under renormings for non-reflexive Banach spaces. This, together with a result by Reich, shows that a Banach space is reflexive if and only if it has the same family of closed convex sets with the almost fixed point property for every equivalent norm. |
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