A local version of a result of Gamlen and Gaudet
type: Item
instance of: scholarly article
title: A local version of a result of Gamlen and Gaudet
zbMATH Open document ID: 0661.46017
DOI: 10.1007/BF02765039
author: Paul F. X. Müller
published in: Israel Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Let D be a subset of the natural numbers and \(X^ p_ D\) the closed linear span in \(L^ P[0,1]\) of the subset \(\{h_ j| j\in D\}\) of the Haar basis \(\{h_ j\}^{\infty}_{j=1}\) for \(L^ p[0,1]\), where \(1<p<+\infty.\) \textit{J. L. B. Gamlen} and \textit{R. J. Gaudet} showed in 1973 that if D is infinite then \(X^ p_ D\) is isomorphic to either \(\ell^ p\) or \(L^ p[0,1]\) [Isr. J. Math. 15, 404-413 (1973; Zbl 0296.46031)]. In this paper it is shown that for any \(1<p<+\infty\) there exists a constant \(K_ p>0\) so that for any finite set D the space \(X^ p_ D\) is \(K_ p\)- isomorphic to \(\ell^ p_{\#D}\), where {\#}D denotes the cardinality of D.
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 4080147
zbMATH Keywords: Haar basis
reviewed by: James R. Holub
MaRDI profile type: Publication
cites work: Extensions of Hardy spaces and their use in analysis
cites work: On subsequences of the Haar system in \(L_p [0,1]\), \((1<p<\infty)\)
cites work: Isomorphismes entre espaces \(H_ 1\)
full work available at URL: https://doi.org/10.1007/bf02765039
OpenAlex ID: W2027696693
description: scientific article; zbMATH DE number 4080147