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
收藏
页码：169 / 178
页数：10
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