On bases in Banach spaces
Volume 170 / 2005
Studia Mathematica 170 (2005), 147-171
MSC: Primary 46B20; Secondary 03E75, 03E35.
DOI: 10.4064/sm170-2-3
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 $\ell _\infty $ as well as in separable Banach spaces.
