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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-2-5,
author = {Juan Carlos Ferrando},
title = {On Hamel bases in Banach spaces},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {169-178},
zbl = {1310.46024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-2-5}
}
Juan Carlos Ferrando. On Hamel bases in Banach spaces. Studia Mathematica, Tome 223 (2014) pp. 169-178. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-2-5/