On Hamel bases in Banach spaces

被引：1

作者：

Carlos Ferrando, Juan ^{[1
]}

机构：

[1] Univ Miguel Hernandez, Ctr Invest Operat, E-03202 Elche, Alicante, Spain

来源：

STUDIA MATHEMATICA | 2014年 / 220卷 / 02期

关键词：

Hamel basis; Banach space; K-analytic space; countably K-determined space; barrelled space;

D O I：

10.4064/sm220-2-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that no infinite-dimensional Banach space can have a weakly K-analytic Hamel basis. As consequences, (i) no infinite-dimensional weakly analytic separable Banach space E has a Hamel basis C-embedded in E(weak), and (ii) no infinite-dimensional Banach space has a weakly pseudocompact Hamel basis. Among other results, it is also shown that there exist noncomplete normed barrelled spaces with closed discrete Hamel bases of arbitrarily large cardinality.

引用

页码：169 / 178

页数：10

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