Banach spaces without minimal subspaces

DOI10.1016/j.jfa.2009.01.028zbMath1181.46004arXiv0711.1350OpenAlexW2024445008MaRDI QIDQ1028338

Christian Rosendal, Valentin Ferenczi

Publication date: 30 June 2009

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

Full work available at URL: https://arxiv.org/abs/0711.1350

zbMATH Keywords

Gowers dichotomyclassification of Banach spacesdichotomiesminimal Banach spacesquasi-minimal subspacetight basis

Mathematics Subject Classification ID

Partial orders, general (06A06) Isomorphic theory (including renorming) of Banach spaces (46B03) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Ramsey theory (05D10)

Related Items (19)

An exact Ramsey principle for block sequences ⋮ Determinacy of adversarial Gowers games ⋮ A weak Hilbert space with few symmetries ⋮ Filters on a countable vector space ⋮ Local Banach-space dichotomies and ergodic spaces ⋮ Geometries of topological groups ⋮ \(\alpha \)-minimal Banach spaces ⋮ Ramsey theory without pigeonhole principle and the adversarial Ramsey principle ⋮ Banach spaces without minimal subspaces -- examples ⋮ A hereditarily indecomposable Banach space with rich spreading model structure ⋮ Isomorphisms and strictly singular operators in mixed Tsirelson spaces ⋮ Strictly singular operators in Tsirelson like spaces ⋮ On uniformly finitely extensible Banach spaces ⋮ Quasi-minimality and tightness by range in spaces with unconditional basis ⋮ Operators in tight by support Banach spaces ⋮ Infinite asymptotic games ⋮ Quasiminimality in mixed Tsirelson spaces ⋮ An extremely non-homogeneous weak Hilbert space ⋮ On the complexity of some inevitable classes of separable Banach spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Banach spaces without minimal subspaces -- examples
• Infinite asymptotic games
• On Tsirelson's space
• An arbitrarily distortable Banach space
• Tsirelson's space. With an appendix by J. Baker, O. Slotterbeck and R. Aron
• Not every Banach space contains an imbedding of \(l_p\) or \(c_0\)
• Sous-espaces de dimension finie des espaces de Banach reticules
• The dimension of almost spherical sections of convex bodies
• Modified mixed Tsirelson spaces
• The distortion problem
• Banach spaces with small spaces of operators
• Unconditional bases and unconditional finite-dimensional decompositions in Banach spaces
• An infinite Ramsey theorem and some Banach-space dichotomies
• Minimal subspaces and isomorphically homogeneous sequences in a Banach space
• Ergodic Banach spaces
• Coding into Ramsey sets
• A new dichotomy for Banach spaces
• Examples of asymptotic ℓ₁ Banach spaces
• The Unconditional Basic Sequence Problem
• Trees and branches in Banach spaces
• On the Existence of Asymptotic-l_p Structures in Banach Spaces
• Minimality properties of Tsirelson type spaces
• The complexity of classifying separable Banach spaces up to isomorphism
• OnB-convex Banach spaces
• A reflexive Banach space which is not sufficiently Euclidean
• Incomparable, non-isomorphic and minimal Banach spaces
• Subsymmetric sequences and minimal spaces
• Selecting basic sequences in φ-stable Banach spaces
• A Solution to Banach's Hyperplane Problem
• A Banach space block finitely universal for monotone bases
• On strongly asymptotic l _p spaces and minimality
• Universal bases
• Weakly Ramsey sets in Banach spaces
• Finite high-order games and an inductive approach towards Gowers's dichotomy

This page was built for publication: Banach spaces without minimal subspaces