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.

引用

页码：2251 / 2280

页数：30

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