Tomek Bartoszyński1, Mirna Džamonja2, Lorenz Halbeisen3, Eva Murtinová4, Anatolij Plichko5
Studia Math. 170 (2005), 147-171
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.
MSC (2000): Primary 46B20; Secondary 03E75, 03E35.
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