Geodesic
On bases in Banach spaces
Tomek Bartoszyński 1   ; Mirna Džamonja 2   ; Lorenz Halbeisen 3   ; Eva Murtinová 4   ; Anatolij Plichko 5
1 Division of Mathematical Sciences National Science Foundation 4201 Wilson Blvd Arlington, VA 22230, U.S.A.
2 School of Mathematics University of East Anglia Norwich, NR4s 7TJ, UK
3 Theoretische Informatik und Logik Universität Bern Neubrückstrasse 10 3012 Bern, Switzerland
4 Department of Math. Analysis Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75 Praha 8, Czech Republic
5 Institute of Mathematics Cracow University of Technology Warszawska 24 31-155 Kraków, Poland
Studia Mathematica, Tome 170 (2005) no. 2, pp. 147-171 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\ell _\infty $ as well as in separable Banach spaces.
DOI : 10.4064/sm170-2-3
Keywords: investigate various kinds bases infinite dimensional banach spaces particular consider complexity hamel bases separable non separable banach spaces separable banach space hamel basis cannot analytic whereas there non separable hilbert spaces which have discrete closed hamel basis further investigate existence certain complete minimal systems ell infty separable banach spaces

Tomek Bartoszyński  1   ; Mirna Džamonja  2   ; Lorenz Halbeisen  3   ; Eva Murtinová  4   ; Anatolij Plichko  5

1 Division of Mathematical Sciences National Science Foundation 4201 Wilson Blvd Arlington, VA 22230, U.S.A.
2 School of Mathematics University of East Anglia Norwich, NR4s 7TJ, UK
3 Theoretische Informatik und Logik Universität Bern Neubrückstrasse 10 3012 Bern, Switzerland
4 Department of Math. Analysis Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75 Praha 8, Czech Republic
5 Institute of Mathematics Cracow University of Technology Warszawska 24 31-155 Kraków, Poland 
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     title = {On bases in {Banach} spaces},
     journal = {Studia Mathematica},
     pages = {147--171},
     year = {2005},
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     doi = {10.4064/sm170-2-3},
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Tomek Bartoszyński; Mirna Džamonja; Lorenz Halbeisen; Eva Murtinová; Anatolij Plichko. On bases in Banach spaces. Studia Mathematica, Tome 170 (2005) no. 2, pp. 147-171. doi: 10.4064/sm170-2-3

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