On bases in Banach spaces

• Autorzy: Tomek Bartoszyński , Mirna Džamonja , Lorenz Halbeisen , Eva Murtinová , Anatolij Plichko
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 03E75: Applications of set theory
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 170
• Numer: 2
• Strony: 147-171

Daty

wydano

2005

Twórcy

autor

Tomek Bartoszyński

• Division of Mathematical Sciences, National Science Foundation, 4201 Wilson Blvd, Arlington, VA 22230, U.S.A.

autor

Mirna Džamonja

• School of Mathematics, University of East Anglia, Norwich, NR4s 7TJ, UK

autor

Lorenz Halbeisen

• Theoretische Informatik und Logik, Universität Bern, Neubrückstrasse 10, 3012 Bern, Switzerland

autor

Eva Murtinová

• Department of Math. Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

autor

Anatolij Plichko

• Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland

Identyfikatory

DOI

10.4064/sm170-2-3