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The convex hull of a Banach-Saks set

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López Abad, J. and Ruiz Bermejo, César and Tradacete Pérez, Pedro (2014) The convex hull of a Banach-Saks set. Journal of Functional Analysis, 266 (4). pp. 2251-2280. ISSN 0022-1236

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022123613002462


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Abstract

A subset A of a Banach space is called Banach–Saks when every sequence in A has a Cesàro convergent subsequence. Our interest here focuses 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.


Item Type:Article
Uncontrolled Keywords:Banach–Saks property; Convex hull; Schreier spaces; Ramsey property
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:32866
Deposited On:25 Aug 2015 08:55
Last Modified:25 Aug 2015 08:55

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