The convex hull of a Banach-Saks set

被引：20
|
作者：
Lopez-Abad, J. [1 ]
Ruiz, C. [2 ]
Tradacete, P. [3 ]
机构：
[1] UAM, Inst Ciencias Matemat ICMAT, CSIC UAM UCM UC3M, Madrid 28049, Spain
[2] Univ Complutense, Fac Matemat, Dept Anal Matemat, E-28040 Madrid, Spain
[3] Univ Carlos III Madrid, Dept Math, Leganes 28911, Madrid, Spain
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2014年 / 266卷 / 04期
关键词：
Banach-Saks property; Convex hull; Schreier spaces; Ramsey property; SUMMABILITY; PROPERTY;
D O I：
10.1016/j.jfa.2013.06.020
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A subset A of a Banach space is called Banach-Saks when every sequence in A has a Cesaro 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. (C) 2013 Elsevier Inc. All rights reserved.
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页码：2251 / 2280
页数：30
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