Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Some remarks on spreading models and mixed Tsirelson spaces


Author: A. Manoussakis
Journal: Proc. Amer. Math. Soc. 131 (2003), 2515-2525
MSC (2000): Primary 46B03, 46B20, 46B45
Published electronically: November 14, 2002
MathSciNet review: 1974650
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Abstract: We prove that if a Banach space with a bimonotone shrinking basis does not contain $\ell_{1}^{\omega}$ spreading models but every block sequence of the basis contains a further block sequence which is a $c-\ell_{1}^{n}$ spreading model for every $n\in\mathbb{N}$, then every subspace has a further subspace which is arbitrarily distortable. We also prove that a mixed Tsirelson space $T[(\mathcal{S}_{n},\theta_{n})_{n}]$, such that $\theta_{n}\searrow 0$, does not contain $\ell_{1}^{\omega2}$ spreading models.


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Additional Information

A. Manoussakis
Affiliation: Department of Sciences, Technical University of Crete, 73100 Chania, Greece
Email: amanouss@science.tuc.gr

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06832-6
Keywords: Schreier families, spreading model
Received by editor(s): November 13, 2001
Received by editor(s) in revised form: March 24, 2002
Published electronically: November 14, 2002
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2002 American Mathematical Society