Symmetric block bases in finite-dimensional normed spaces
type: Item
instance of: scholarly article
title: Symmetric block bases in finite-dimensional normed spaces
zbMATH Open document ID: 0716.46015
DOI: 10.1007/BF02772661
published in: Israel Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: It is shown that for \(1\leq p<\infty\) and \(\epsilon\in]0,[\) any basis of \(\ell^ n_ p\), which is C-equivalent to the unit vector basis of \(\ell^ n_ p\) has a \((1+\epsilon)\)-symmetric block basis of cardinality proportional to n/log n, where the proportionality factor only depends on C, \(\epsilon\) and p. When \(1<p<\infty\), an upper bound proportional to n log log n/log n of such \((1+\epsilon)\)-symmetric block bases is also obtained. The proofs are based on measure theoretic methods and the results generalize results of \textit{D. Amir} and \textit{V. D. Milman} [Isr. J. Math. 50, 1-12 (1985; Zbl 0612.46021)].
Mathematics Subject Classification ID: 46B15
zbMATH DE Number: 4180087
zbMATH Keywords: C-equivalent to the unit vector basis
zbMATH Keywords: symmetric block basis
zbMATH Keywords: measure theoretic methods
author: W. Timothy Gowers
reviewed by: Martin Schottenloher
MaRDI profile type: Publication
cites work: Unconditional and symmetric sets in \(n\)-dimensional normed spaces
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cites work: Q3682518
cites work: Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach
cites work: Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
description: scientific article; zbMATH DE number 4180087