Banach spaces without minimal subspaces -- examples
type: Item
instance of: scholarly article
title: Banach spaces without minimal subspaces -- examples
zbMATH Open document ID: 1254.46011
author: Valentin Ferenczi
author: Christian Rosendal
publication date: 2012-08-22T00:00:00Z
full work available at URL: https://arxiv.org/abs/1104.4724
review text: As a consequence of several dichotomies, there is a chart of 19 inevitable classes (derived from \textit{V. Ferenczi} and \textit{C. Rosendal} [J. Funct. Anal. 257, No. 1, 149--193 (2009; Zbl 1181.46004)]) so that any infinite-dimensional Banach space contains a subspace of one of these classes. This interesting paper presents several new examples of Banach spaces corresponding to these classes. The final section contains various challenging open problems; for instance, to find the exact position of Argyros-Haydon's famous space in the aforementioned chart.
Mathematics Subject Classification ID: 46B03
Mathematics Subject Classification ID: 03E15
zbMATH DE Number: 6069842
zbMATH Keywords: classification of Banach spaces
zbMATH Keywords: dichotomies
zbMATH Keywords: tight Banach spaces
reviewed by: Daniel Pellegrino
MaRDI profile type: Publication
OpenAlex ID: W1838639657
arXiv ID: 1104.4724
cites work: An extremely non-homogeneous weak Hilbert space
cites work: A weak Hilbert space with few symmetries
cites work: Examples of asymptotic ℓ₁ Banach spaces
cites work: Modified mixed Tsirelson spaces
cites work: A hereditarily indecomposable \(\mathcal L_{\infty}\)-space that solves the scalar-plus-compact problem
cites work: Q3134757
cites work: Q4283364
cites work: Tsirelson's space. With an appendix by J. Baker, O. Slotterbeck and R. Aron
cites work: On strongly asymptotic l p spaces and minimality
cites work: Ergodic Banach spaces
cites work: Banach spaces without minimal subspaces
cites work: A Solution to Banach's Hyperplane Problem
cites work: Q4839524
cites work: A new dichotomy for Banach spaces
cites work: An infinite Ramsey theorem and some Banach-space dichotomies
cites work: The Unconditional Basic Sequence Problem
cites work: Minimality properties of Tsirelson type spaces
cites work: An arbitrarily distortable Banach space
cites work: On the Existence of Asymptotic-lp Structures in Banach Spaces
cites work: Not every Banach space contains an imbedding of \(l_p\) or \(c_0\)
DOI: 10.5802/AIF.2684
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 6069842