On bases in Banach spaces

Tomek Bartoszynski, Mirna Džamonja, Lorenz Halbeisen, Eva Murtinova, Anatolij Plichko

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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 ℓ∞ as well as in separable Banach spaces.
Original languageEnglish
Pages (from-to)147-171
Number of pages25
JournalStudia Mathematica
Volume170
Issue number2
DOIs
Publication statusPublished - 2005

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