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On Antichains of Spreading Models of Banach Spaces

Published online by Cambridge University Press:  20 November 2018

Pandelis Dodos
Pandelis Dodos*
Affiliation:
National Technical University of Athens, Faculty of Applied Sciences, Department of Mathematics, Zografou Campus, 157 80, Athens, Greece e-mail: pdodos@math.ntua.gr
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Abstract

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We show that for every separable Banach space $X$, either $\text{S}{{\text{P}}_{w}}\left( X \right)$ (the set of all spreading models of $X$ generated by weakly-null sequences in $X$, modulo equivalence) is countable, or $\text{S}{{\text{P}}_{w}}\left( X \right)$ contains an antichain of the size of the continuum. This answers a question of S. J. Dilworth, E. Odell, and B. Sari.

Keywords

46B2003E15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 1 , 01 March 2010 , pp. 64 - 76
Copyright
Copyright © Canadian Mathematical Society 2010

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