Concerning the Szlenk index

DOI10.4064/sm8197-10-2016zbMath1369.46007arXiv1501.06885OpenAlexW2963606043MaRDI QIDQ2957285

Ryan M. Causey

Publication date: 25 January 2017

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.06885

zbMATH Keywords

Ramsey theoryuniversalitySzlenk indexembedding in spaces with finite-dimensional decompositions

Mathematics Subject Classification ID

Isomorphic theory (including renorming) of Banach spaces (46B03) Spaces of operators; tensor products; approximation properties (46B28)

Related Items (14)

Direct sums and summability of the Szlenk index ⋮ The complexity of some ordinal determined classes of operators ⋮ Uniform subsequential estimates on weakly null sequences ⋮ Algebras of diagonal operators of the form scalar-plus-compact are Calkin algebras ⋮ Isometries of combinatorial Tsirelson spaces ⋮ Non-three space properties and Szlenk index ⋮ Proximity to \(\ell_p\) and \(c_0\) in Banach spaces ⋮ On isometries and Tingley’s problem for the spaces $T[\theta , \mathcal{S}_{\alpha }$, $1 \leqslant\alpha \lt \omega _{1}$] ⋮ \(\xi\)-completely continuous operators and \(\xi\)-Schur Banach spaces ⋮ On the geometry of higher order Schreier spaces ⋮ Prescribed Szlenk index of separable Banach spaces ⋮ Factorization of Asplund operators ⋮ A ξ-weak Grothendieck compactness principle ⋮ Uniform upper estimates and the repeated averages hierarchy

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Three-space property for asymptotically uniformly smooth renormings
• Partition theorems for systems of finite subsets of integers
• Concerning Bourgain's \(\ell_1\)-index of a Banach space
• Ramsey methods in analysis
• The Bourgain \(\ell^{1}\)-index of mixed Tsirelson space
• On Zippin's embedding theorem of Banach spaces into Banach spaces with bases
• Uniformly non-square Banach spaces
• The Szlenk index and local \(\ell_1\)-indices
• Conditional weak compactness in certain inductive tensor products
• Estimation of the Szlenk index of Banach spaces via Schreier spaces
• Estimation of the Szlenk index of reflexive Banach spaces using generalized Baernstein spaces
• Asplund operators and the Szlenk index
• Banach spaces of bounded Szlenk index II
• Some strongly bounded classes of Banach spaces
• A Characterization of Banach Spaces Containing l ¹
• A dichotomy theorem for subsets of the power set of the natural numbers
• Banach spaces of bounded Szlenk index
• The non-existence of a separable reflexive Banach space universal for all separable reflexive Banach spaces

This page was built for publication: Concerning the Szlenk index