On a problem by N. Kalton and the space \(l^p(I)\)
type: Item
instance of: scholarly article
title: On a problem by N. Kalton and the space \(l^p(I)\)
zbMATH Open document ID: 1162.46006
author: Nuno C. Freire
author: M. F. Veiga
published in: Acta Mathematica Vietnamica
publication date: 2008-10-20T00:00:00Z
review text: The authors claim to have proved that every infinite-dimensional quasi-Banach space contains a proper closed infinite-dimensional subspace; this is a major open problem in the theory of these spaces. However, their argument is incorrect since it is built on the erroneous assumption that a continuous surjection between dense subspaces of quasi-Banach spaces \(X\) and \(Y\) extends to a continuous surjection between \(X\) and \(Y\) themselves. The paper also contains an incorrect proof of the known fact that \(L_p[0,1]\) is primary for \(0<p<1\).
reviewed by: Dirk Werner
Mathematics Subject Classification ID: 46A16
zbMATH DE Number: 5354277
zbMATH Keywords: quasi-Banach spaces
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5354277