Approximation of Lipschitz functions by Δ-convex functions in banach spaces
In this paper we give some results about the approximation of a Lipschitz function on a Banach space by means of ∆-convex functions. In particular, we prove that the density of ∆-convex functions in the set of Lipschitz functions for the topology of uniform convergence on bounded sets characterizes...
| Autor: | |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 1998 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/43521 |
| Acceso en línea: | http://hdl.handle.net/11441/43521 https://doi.org/10.1007/BF02773472 |
| Access Level: | acceso abierto |
| Palabra clave: | Convex functions Superreflexivity in Banach spaces |
| Sumario: | In this paper we give some results about the approximation of a Lipschitz function on a Banach space by means of ∆-convex functions. In particular, we prove that the density of ∆-convex functions in the set of Lipschitz functions for the topology of uniform convergence on bounded sets characterizes the superreflexivity of the Banach space. We also show that Lipschitz functions on superreflexive Banach spaces are uniform limits on the whole space of ∆-convex functions. |
|---|