The average distance property of classical Banach spaces II
Functional Analysis
2007-05-23 v1
Abstract
A Banach space X has the average distance property (ADP) if there exists a unique real number r such that for each positive integer n and all x_1,...,x_n in the unit sphere of X there is some x in the unit sphere of X such that 1/n \sum_{k=1}^n ||x_k-x|| = r. We show that l_p does not have the average distance property if p>2. This completes the study of the ADP for l_p spaces.
Cite
@article{arxiv.math/0202093,
title = {The average distance property of classical Banach spaces II},
author = {Aicke Hinrichs and J. Wenzel},
journal= {arXiv preprint arXiv:math/0202093},
year = {2007}
}
Comments
10 pages, to appear in Bull. Austr. Math. Soc