Approximation of Lipschitz functions by $\Delta$-convex functions in Banach spaces
Functional Analysis
2009-09-25 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/9702212,
title = {Approximation of Lipschitz functions by $\Delta$-convex functions in Banach spaces},
author = {Manuel Cepedello Boiso},
journal= {arXiv preprint arXiv:math/9702212},
year = {2009}
}