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On bases in Banach spaces

Tomek Bartoszyński;  Mirna Džamonja;  Lorenz Halbeisen;  Eva Murtinová;  Anatolij Plichko — 2005

Studia Mathematica

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.

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