Ferenczi, Valentin and Pelczar, Anna Maria and Rosendal, Christian (2004) On a Question of Haskell P. Rosenthal Concerning a Characterization of c_0 and ℓ_p. Bulletin of the London Mathematical Society, 36 . pp. 396-406. ISSN 0024-6093 http://resolver.caltech.edu/CaltechAUTHORS:20110823-081619620
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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 ℓ_p. An analogous problem concerning spreading models is also addressed.
|Additional Information:||© 2011 London Mathematical Society. Received 12 December 2002; revised 17 June 2003. 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. We wish to thank G. Androulakis and T. Schlumprecht for useful information about spreading models, and for their comments about this paper. We are grateful to the reviewer for valuable remarks.|
|Classification Code:||2000 Mathematics Subject Classification: 46B20 (primary), 46B15 (secondary).|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||13 Sep 2011 16:41|
|Last Modified:||26 Dec 2012 13:30|
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