[Banach] Abstract of a paper by C. Ruiz, J. Lopez-Abad and P. Tradacete

This is an announcement for the paper "The convex hull of a Banach-Saks set" by C. Ruiz, J. Lopez-Abad and P. Tradacete.

Abstract: A subset $A$ of a Banach space is called Banach-Saks when every sequence in $A$ 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.

Archive classification: math.FA math.CO math.LO

Mathematics Subject Classification: 46B50, 05D10

Remarks: 29 pages

Submitted from: abad@icmat.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1209.4851

or

http://arXiv.org/abs/1209.4851