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

Algebra, Number Theory, Logic, and Representations (ANTLR)

Research output: Contribution to journal › Article › peer-review

21 Downloads (Pure)

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

Access to Document

10.4064/sm170-2-3

metal.psOther version, 542 KB

Cite this

@article{0929da0b8e4446eaae2167cfed723ef7,

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.",

author = "Tomek Bartoszynski and Mirna D{\v z}amonja and Lorenz Halbeisen and Eva Murtinova and Anatolij Plichko",

year = "2005",

doi = "10.4064/sm170-2-3",

language = "English",

volume = "170",

pages = "147--171",

journal = "Studia Mathematica",

publisher = "Institute of Mathematics, Polish Academy of Sciences",

number = "2",

}

TY - JOUR

T1 - On bases in Banach spaces

AU - Bartoszynski, Tomek

AU - Džamonja, Mirna

AU - Halbeisen, Lorenz

AU - Murtinova, Eva

AU - Plichko, Anatolij

PY - 2005

Y1 - 2005

N2 - 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.

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.

U2 - 10.4064/sm170-2-3

DO - 10.4064/sm170-2-3

M3 - Article

VL - 170

SP - 147

EP - 171

JO - Studia Mathematica

JF - Studia Mathematica

IS - 2

ER -