ℓ¹-Spreading models in subspaces of mixed Tsirelson spaces

• Autorzy: Denny H. Leung , Wee-Kee Tang
• Języki publikacji: EN

Abstrakty

EN

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 $X = T[(θₙ,𝓢ₙ)^{∞}_{n=1}]$:
(1) Every block subspace of X contains an $ℓ¹-𝓢_{ω}$-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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B15: Summability and bases
• 46B07: Local theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 172
• Numer: 1
• Strony: 47-68

Daty

wydano

2006

Twórcy

autor

Denny H. Leung

• Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543

autor

Wee-Kee Tang

• Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616

Identyfikatory

DOI

10.4064/sm172-1-3