ℓ¹-Spreading models in subspaces of mixed Tsirelson spaces

Denny H. Leung; Wee-Kee Tang

Studia Mathematica, Tome 173 (2006), p. 47-68 / Harvested from The Polish Digital Mathematics Library

Résumé

We investigate the existence of higher order ℓ¹-spreading models in subspaces of mixed Tsirelson spaces. For instance, we show that the following conditions are equivalent for the mixed Tsirelson space $X = T [{(θ ₙ, ₙ)}_{n = 1}^{\infty}]$ : (1) Every block subspace of X contains an $ℓ ¹ -_{ω}$ -spreading model, (2) The Bourgain ℓ¹-index $I_{b} (Y) = I (Y) > ω^{ω}$ for any block subspace Y of X, (3) $l i m ₘ l i m s u p ₙ θ_{m + n} / θ ₙ > 0$ and every block subspace Y of X contains a block sequence equivalent to a subsequence of the unit vector basis of X. Moreover, if one (and hence all) of these conditions holds, then X is arbitrarily distortable.

Publié le : 2006-01-01

Zbl 1101.46004

EUDML-ID : urn:eudml:doc:284774

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     title = {l1-Spreading models in subspaces of mixed Tsirelson spaces},
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Denny H. Leung; Wee-Kee Tang. ℓ¹-Spreading models in subspaces of mixed Tsirelson spaces. Studia Mathematica, Tome 173 (2006) pp. 47-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-1-3/