On Hamel bases in Banach spaces
Volume 220 / 2014
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.
