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Unconditional structures of weakly null sequences


Authors: S. A. Argyros and I. Gasparis
Journal: Trans. Amer. Math. Soc. 353 (2001), 2019-2058
MSC (2000): Primary 46B03; Secondary 06A07, 03E10
DOI: https://doi.org/10.1090/S0002-9947-01-02711-8
Published electronically: January 10, 2001
MathSciNet review: 1813606
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Abstract:

The following dichotomy is established for a normalized weakly null sequence in a Banach space: Either every subsequence admits a convex block subsequence equivalent to the unit vector basis of $c_0$, or there exists a subsequence which is boundedly convexly complete.


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Additional Information

S. A. Argyros
Affiliation: Department of Mathematics, University of Athens, Athens 15784, Greece
Address at time of publication: Department of Mathematics, National Technical University of Athens, 15780 Athens, Greece
Email: sargyros@math.ntua.gr

I. Gasparis
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078-1058
Email: ioagaspa@math.okstate.edu

DOI: https://doi.org/10.1090/S0002-9947-01-02711-8
Keywords: Ramsey theory, weakly null sequence, convex block basis
Received by editor(s): November 20, 1998
Received by editor(s) in revised form: February 14, 2000
Published electronically: January 10, 2001
Article copyright: © Copyright 2001 American Mathematical Society

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