On bases in Banach spaces

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

doi:10.4064/sm170-2-3

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 language	English
Pages (from-to)	147-171
Number of pages	25
Journal	Studia Mathematica
Volume	170
Issue number	2
DOIs	https://doi.org/10.4064/sm170-2-3
Publication status	Published - 2005

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title = "On bases in Banach spaces",

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.",

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AU - Halbeisen, Lorenz

AU - Murtinova, Eva

AU - Plichko, Anatolij

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AB - 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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