The Bourgain \(\ell^{1}\)-index of mixed Tsirelson space

DOI10.1016/S0022-1236(02)00171-4zbMath1028.46021arXivmath/0110154MaRDI QIDQ1874694

Wee-Kee Tang, Denny H. Leung

Publication date: 25 May 2003

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0110154

zbMATH Keywords

Schreier familiesBourgain's \(\ell^1\)-indexMixed Tsirelson space

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Isomorphic theory (including renorming) of Banach spaces (46B03)

Related Items

Operators on $C(K)$ spaces preserving copies of Schreier spaces, Concerning the Szlenk index, The universality of \(\ell _{1}\) as a dual space, \(\ell^1\)-spreading models in mixed Tsirelson space, More mixed Tsirelson spaces that are not isomorphic to their modified versions, Uniform upper estimates and the repeated averages hierarchy, The $\ell ^{1}$-indices of Tsirelson type spaces

Cites Work

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• On Tsirelson's space
• Tsirelson superspaces and \(\ell _ p\)
• Modified mixed Tsirelson spaces
• Concerning Bourgain's \(\ell_1\)-index of a Banach space
• Distorting mixed Tsirelson spaces
• Proximity to \(\ell_ 1\) and distortion in asymptotic \(\ell_ 1\) spaces
• On certain equivalent norms on Tsirelson's space
• The Szlenk index and local \(\ell_1\)-indices
• Examples of asymptotic ℓ₁ Banach spaces
• A dichotomy theorem for subsets of the power set of the natural numbers
• The $\ell ^{1}$-indices of Tsirelson type spaces
• l¹-Spreading models in subspaces of mixed Tsirelson spaces