Lipschitz functions on classical spaces
type: Item
instance of: scholarly article
title: Lipschitz functions on classical spaces
zbMATH Open document ID: 0763.46015
DOI: 10.1016/0195-6698(92)90020-Z
published in: European Journal of Combinatorics
publication date: 1992-09-27T00:00:00Z
review text: It is shown that if \(f\) is a Lipschitz function defined on the unit sphere of \(c_ 0\), then for every positive \(\varepsilon\) there is an infinite dimensional subspace of \(c_ 0\) on whose unit sphere \(f\) differs by less than \(\varepsilon\). The theorem is related to the open question if every space isomorphic to \(\ell_ p\) (for \(1<p<\infty\)) contains a subspace that is \((1+\varepsilon)\) isomorphic to \(\ell_ p\).
reviewed by: Daniel Wulbert
Mathematics Subject Classification ID: 46B25
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 05D10
zbMATH DE Number: 64840
zbMATH Keywords: isomorphic properties of \(\ell_ p\)
zbMATH Keywords: Lipschitz function
zbMATH Keywords: \((1+\varepsilon)\) isomorphic
author: W. Timothy Gowers
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 64840