Good \(\ell_2\)-subspaces of \(L_p\), \(p>2\)
type: Item
instance of: scholarly article
title: Good \(\ell_2\)-subspaces of \(L_p\), \(p>2\)
zbMATH Open document ID: 1194.46014
author: Dale Alspach
published in: Banach Journal of Mathematical Analysis
publication date: 2010-04-27T00:00:00Z
full work available at URL: https://eudml.org/doc/231939
full work available at URL: tex v3 n2 a6.pdf
review text: In a recent preprint, \textit{R.\,Haydon, E.\,Odell} and \textit{Th.\,Schlumprecht} [``Small subspaces of \(L_p\),'' \url{arXiv:0711.3919}] show that a Hilbertian subspace of \(L_p\), \(p>2\), contains a further subspace \(Z\) that is \((1+\varepsilon)\)-isomorphic to \(\ell_2\) and complemented in \(L_p\) by a projection of norm \(\leq (1+\varepsilon)\gamma_p\), where \(\gamma_p\) is the \(L_p\)-norm of a standard Gaussian random variable. Their proof uses random measures and types à la Krivine and Maurey. Here, the author gives another proof that avoids these means and depends only on a version of the central limit theorem for martingales.
reviewed by: Dirk Werner
Mathematics Subject Classification ID: 46B09
Mathematics Subject Classification ID: 46B25
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 5702385
zbMATH Keywords: subspaces of \(L_p\)
zbMATH Keywords: well complemented subspace
zbMATH Keywords: Hilbertian subspace
zbMATH Keywords: central limit theorem
MaRDI profile type: Publication
OpenAlex ID: W1977147948
DOI: 10.15352/BJMA/1261086708
description: scientific article; zbMATH DE number 5702385