ℓ¹-Spreading models in subspaces of mixed Tsirelson spaces

Denny H. Leung, and Wee-Kee Tang. "ℓ¹-Spreading models in subspaces of mixed Tsirelson spaces." Studia Mathematica 172.1 (2006): 47-68. <http://eudml.org/doc/284774>.

@article{DennyH2006,
abstract = {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 $X = T[(θₙ,ₙ)^\{∞\}_\{n=1\}]$: (1) Every block subspace of X contains an $ℓ¹-_\{ω\}$-spreading model, (2) The Bourgain ℓ¹-index $I_\{b\}(Y) = I(Y) > ω^\{ω\}$ for any block subspace Y of X, (3) $limₘ lim supₙ θ_\{m+n\}/θₙ > 0$ 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.},
author = {Denny H. Leung, Wee-Kee Tang},
journal = {Studia Mathematica},
keywords = {mixed Tsirelson space; --spreading model; arbitrarily distortable Banach space; Bourgain’s index},
language = {eng},
number = {1},
pages = {47-68},
title = {ℓ¹-Spreading models in subspaces of mixed Tsirelson spaces},
url = {http://eudml.org/doc/284774},
volume = {172},
year = {2006},
}

TY - JOUR
AU - Denny H. Leung
AU - Wee-Kee Tang
TI - ℓ¹-Spreading models in subspaces of mixed Tsirelson spaces
JO - Studia Mathematica
PY - 2006
VL - 172
IS - 1
SP - 47
EP - 68
AB - 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 $X = T[(θₙ,ₙ)^{∞}_{n=1}]$: (1) Every block subspace of X contains an $ℓ¹-_{ω}$-spreading model, (2) The Bourgain ℓ¹-index $I_{b}(Y) = I(Y) > ω^{ω}$ for any block subspace Y of X, (3) $limₘ lim supₙ θ_{m+n}/θₙ > 0$ 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.
LA - eng
KW - mixed Tsirelson space; --spreading model; arbitrarily distortable Banach space; Bourgain’s index
UR - http://eudml.org/doc/284774
ER -