The convex hull of a Banach-Saks set
Functional Analysis
2012-09-24 v1 Combinatorics
Logic
Abstract
A subset of a Banach space is called Banach-Saks when every sequence in has a Ces{\`a}ro convergent subsequence. Our interest here focusses on the following problem: is the convex hull of a Banach-Saks set again Banach-Saks? By means of a combinatorial argument, we show that in general the answer is negative. However, sufficient conditions are given in order to obtain a positive result.
Cite
@article{arxiv.1209.4851,
title = {The convex hull of a Banach-Saks set},
author = {C. Ruiz and J. Lopez-Abad and P. Tradacete},
journal= {arXiv preprint arXiv:1209.4851},
year = {2012}
}
Comments
29 pages