Geodesic
On Hamel bases in Banach spaces
Juan Carlos Ferrando1
1 Centro de Investigación Operativa Edificio Torretamarit, Avda de la Universidad s/n Universidad Miguel Hernández E-03202 Elche (Alicante), Spain
Studia Mathematica, Tome 220 (2014) no. 2, pp. 169-178

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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( \mathrm {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.
DOI : 10.4064/sm220-2-5
Keywords: shown infinite dimensional banach space have weakly k analytic hamel basis consequences infinite dimensional weakly analytic separable banach space has hamel basis c embedded mathrm weak infinite dimensional banach space has weakly pseudocompact hamel basis among other results shown there exist noncomplete normed barrelled spaces closed discrete hamel bases arbitrarily large cardinality

Juan Carlos Ferrando 1

1 Centro de Investigación Operativa Edificio Torretamarit, Avda de la Universidad s/n Universidad Miguel Hernández E-03202 Elche (Alicante), Spain 
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Juan Carlos Ferrando. On Hamel bases in Banach spaces. Studia Mathematica, Tome 220 (2014) no. 2, pp. 169-178. doi: 10.4064/sm220-2-5

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