Transfinite almost square Banach spaces

被引：1

作者：

Aviles, Antonio ^{[1
]}

Ciaci, Stefano ^{[3
]}

Langemets, Johann ^{[3
]}

Lissitsin, Aleksei ^{[3
]}

Zoca, Abraham Rueda ^{[2
]}

机构：

[1] Univ Murcia, Dept Matemat, Campus Espinardo, Murcia 30100, Spain

[2] Univ Granada, Fac Ciencias, Dept Anal Matemat, Granada 18071, Spain

[3] Univ Tartu, Inst Math & Stat, EE-51009 Tartu, Estonia

来源：

STUDIA MATHEMATICA | 2023年 / 271卷 / 01期

关键词：

c0(?); almost square space; octahedral norm; renorming; OCTAHEDRAL NORMS; TENSOR-PRODUCTS;

D O I：

10.4064/sm220517-4-11

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Is is known that a Banach space contains an isomorphic copy of c0 if, and only if, it can be equivalently renormed to be almost square. We introduce and study transfinite versions of almost square Banach spaces with the purpose of relating them to the containment of isomorphic copies of c0(kappa), where kappa is some uncountable cardinal. We also provide several examples and stability results for the above properties by taking direct sums, tensor products and ultraproducts. By connecting the above properties with transfinite analogues of the strong diameter 2 property and octahedral norms, we obtain a solution to an open question of Ciaci et al. [Israel J. Math. (online, 2022)].

引用

页码：39 / 63

页数：25

共 27 条

[1] Almost square dual Banach spaces [J].