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On Hamel bases in Banach spaces

Volume 220 / 2014

Juan Carlos Ferrando Studia Mathematica 220 (2014), 169-178 MSC: 46B20, 46A03, 54C35. DOI: 10.4064/sm220-2-5

Abstract

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.

Authors

  • Juan Carlos FerrandoCentro de Investigación Operativa
    Edificio Torretamarit, Avda de la Universidad s/n
    Universidad Miguel Hernández
    E-03202 Elche (Alicante), Spain
    e-mail

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