Some remarks on spreading models and mixed Tsirelson spaces

Manoussakis, A.

doi:10.1090/S0002-9939-02-06832-6

Some remarks on spreading models and mixed Tsirelson spaces
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by A. Manoussakis

Proc. Amer. Math. Soc. 131 (2003), 2515-2525

DOI: https://doi.org/10.1090/S0002-9939-02-06832-6

Published electronically: November 14, 2002

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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 $\ell _{1}^{\omega 2}$ spreading models.

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