On bases in Banach spaces

Tomek Bartoszyński, et al. "On bases in Banach spaces." Studia Mathematica 170.2 (2005): 147-171. <http://eudml.org/doc/284564>.

@article{TomekBartoszyński2005,
abstract = {We investigate various kinds of bases in infinite-dimensional Banach spaces. In particular, we consider the complexity of Hamel bases in separable and non-separable Banach spaces and show that in a separable Banach space a Hamel basis cannot be analytic, whereas there are non-separable Hilbert spaces which have a discrete and closed Hamel basis. Further we investigate the existence of certain complete minimal systems in $ℓ_\{∞\}$ as well as in separable Banach spaces.},
author = {Tomek Bartoszyński, Mirna Džamonja, Lorenz Halbeisen, Eva Murtinová, Anatolij Plichko},
journal = {Studia Mathematica},
keywords = {Hamel basis; minimal system; finitary basis; analytic set; Auerbach basis},
language = {eng},
number = {2},
pages = {147-171},
title = {On bases in Banach spaces},
url = {http://eudml.org/doc/284564},
volume = {170},
year = {2005},
}

TY - JOUR
AU - Tomek Bartoszyński
AU - Mirna Džamonja
AU - Lorenz Halbeisen
AU - Eva Murtinová
AU - Anatolij Plichko
TI - On bases in Banach spaces
JO - Studia Mathematica
PY - 2005
VL - 170
IS - 2
SP - 147
EP - 171
AB - We investigate various kinds of bases in infinite-dimensional Banach spaces. In particular, we consider the complexity of Hamel bases in separable and non-separable Banach spaces and show that in a separable Banach space a Hamel basis cannot be analytic, whereas there are non-separable Hilbert spaces which have a discrete and closed Hamel basis. Further we investigate the existence of certain complete minimal systems in $ℓ_{∞}$ as well as in separable Banach spaces.
LA - eng
KW - Hamel basis; minimal system; finitary basis; analytic set; Auerbach basis
UR - http://eudml.org/doc/284564
ER -