abstract
On bases in Banach spaces
Tomek Bartoszynski, Mirna Dzamonja, Lorenz Halbeisen, Eva Murtinova,
Anatolij Plichko
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 the Banach space of bounded sequences as well as in
separable Banach spaces.