Types et suites symétriques dans \(L^ p\), \(1\leq p<+\infty\), p\(\neq 2\). (Types and symmetric sequences in \(L^ p\), \(1\leq p<+\infty\), p\(\neq 2)\)
type: Item
instance of: scholarly article
title: Types et suites symétriques dans \(L^ p\), \(1\leq p<+\infty\), p\(\neq 2\). (Types and symmetric sequences in \(L^ p\), \(1\leq p<+\infty\), p\(\neq 2)\)
zbMATH Open document ID: 0594.46015
DOI: 10.1007/BF02772858
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: We prove that every normalized sequence in \(L^ p\), weakly null if \(p>2\) and equivalent to the unit vector basis of \(\ell^ 2\) if \(1\leq p<2\), has for all \(\epsilon >0\) a subsequence which is \(2(1+\epsilon)\)-symmetric. This result was known for \(p=1\) (H. P. Rosenthal) and \(p\in 2{\mathbb{N}}\) (W. B. Johnson, B. Maurey, G. Shechtman, L. Tzafriri). Here, we use the techniques of stability which were introduced by J. L. Krivine and B. Maurey: as well as providing new results, this approach unifies and simplifies previous known results.
Mathematics Subject Classification ID: 46B25
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B15
zbMATH DE Number: 3955709
zbMATH Keywords: symmetric sequences
zbMATH Keywords: type on a stable space
zbMATH Keywords: normalized sequence in \(L^ p\)
author: Sylvie Guerre-Delabriere
MaRDI profile type: Publication
cites work: OnB-convex Banach spaces
cites work: Q4087771
cites work: Symmetric structures in Banach spaces
cites work: Bases, lacunary sequences and complemented subspaces in the spaces $L_{p}$
cites work: Espaces de Banach stables
cites work: On subspaces of L\(^p\)
description: scientific article; zbMATH DE number 3955709