On weak compactness in projective tensor products

被引：1
|
作者：
Rodriguez, Jose [1 ]
机构：
[1] Univ Murcia, Fac Informat, Dept Ingn & Tecnol Comp, Espinardo 30100, Murcia, Spain
来源：
QUARTERLY JOURNAL OF MATHEMATICS | 2023年 / 74卷 / 02期
关键词：
BANACH-SPACES; SETS; SEQUENCES; PROPERTY;
D O I：
10.1093/qmath/haac036
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the property of being strongly weakly compactly generated (and some relatives) in projective tensor products of Banach spaces. Our main result is as follows. Let 1 < p,q < infinity be such that 1/p + 1/q >= 1. Let X (resp., Y) be a Banach space with a countable unconditional finite-dimensional Schauder decomposition having a disjoint lower p-estimate (resp., q-estimate). If X and Y are strongly weakly compactly generated, then so is their projective tensor product X circle times circumflex expressionccent pi Y.
引用
收藏
页码：593 / 605
页数：13
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