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arXiv · 1209.4851

The convex hull of a Banach-Saks set

C. Ruiz·J. Lopez-Abad·P. Tradacete
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Abstract

A subset $A$ of a Banach space is called Banach-Saks when every sequence in $A$ has a Ces{à}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.

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C. Ruiz, J. Lopez-Abad, P. Tradacete. 2012-09-21. The convex hull of a Banach-Saks set. https://arxiv.org/abs/1209.4851

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