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ON A QUESTION OF HASKELL P. ROSENTHAL CONCERNING A CHARACTERIZATION OF ${c}_{0}$ AND ${\ell}_{p}$

Published online by Cambridge University Press:  28 April 2004

VALENTIN FERENCZI ,
ANNA MARIA PELCZAR  and
CHRISTIAN ROSENDAL
VALENTIN FERENCZI
Affiliation:
Equipe d'Analyse, Boite 186, Université Paris 6, 4, place Jussieu, 75252 Paris Cedex 05, Franceferenczi@ccr.jussieu.fr
ANNA MARIA PELCZAR
Affiliation:
Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Polandapelczar@im.uj.edu.pl
CHRISTIAN ROSENDAL
Affiliation:
Equipe d'Analyse, Boite 186, Université Paris 6, 4, place Jussieu, 75252 Paris Cedex 05, Franceferenczi@ccr.jussieu.fr Mathematics 253-37, Caltech, Pasadena, CA 91125, USArosendal@ccr.jussieu.fr
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Abstract

The following property of a normalized basis in a Banach space is considered: any normalized block sequence of the basis has a subsequence equivalent to the basis. Under uniformity or other natural assumptions, a basis with this property is equivalent to the unit vector basis of $c_0$ or $\ell_p$. An analogous problem concerning spreading models is also addressed.

Keywords

46B20 (primary)46B15 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 3 , May 2004 , pp. 396 - 406
Copyright
© The London Mathematical Society 2004

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Footnotes

The paper was written during a stay of the second author at the Université Paris 6 within the EU Research Training Network HPRN-CT-2000-00116, a visit by the first author to Kraków, and a visit by all the authors to the Fields Institute during the Set Theory and Analysis Programme, 2002.