Abstrakt
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 $l^\infty$ as well as in separable Banach spaces.