Concerning Bourgain's \(\ell_1\)-index of a Banach space

DOI10.1007/BF02783046zbMath0960.46013arXivmath/9606209MaRDI QIDQ1282272

Edward Odell, Robert P. Judd

Publication date: 2 January 2000

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9606209

zbMATH Keywords

ordinal treesTsirelson spacesBourgain's \(\ell_1\)-index

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Classical Banach spaces in the general theory (46B25)

Related Items

The Bourgain \(\ell^{1}\)-index of mixed Tsirelson space, Arbitrarily distortable Banach spaces of higher order, Weak$^*$ closures and derived sets for convex sets in dual Banach spaces, Operators on $C(K)$ spaces preserving copies of Schreier spaces, Proximity to \(\ell_ 1\) and distortion in asymptotic \(\ell_ 1\) spaces, Estimation of the Szlenk index of reflexive Banach spaces using generalized Baernstein spaces, Quantification of Banach-Saks properties of higher orders, Proximity to \(\ell_p\) and \(c_0\) in Banach spaces, Concerning the Szlenk index, The universality of \(\ell _{1}\) as a dual space, The Szlenk index of injective tensor products and convex hulls, \(\ell^1\)-spreading models in mixed Tsirelson space, On the hereditary proximity to \(\ell _{1}\), The Szlenk index and local \(\ell_1\)-indices, Classes of operators determined by ordinal indices, A ξ-weak Grothendieck compactness principle, The $\ell ^{1}$-indices of Tsirelson type spaces

Cites Work

• Nouvelle demonstration d'un théorème de J. L. Krivine sur la finie représentation de \(l_ p\) dans un espace de Banach
• Not every Banach space contains an imbedding of \(l_p\) or \(c_0\)
• Sous-espaces de dimension finie des espaces de Banach reticules
• On a theorem of J. L. Krivine concerning block finite representability of \(\ell^p\) general Banach spaces
• The distortion problem
• Proximity to \(\ell_ 1\) and distortion in asymptotic \(\ell_ 1\) spaces
• Uniformly non-square Banach spaces
• The non-existence of a separable reflexive Banach space universal for all separable reflexive Banach spaces
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