A characterization of normed spaces
type: Item
instance of: scholarly article
title: A characterization of normed spaces
zbMATH Open document ID: 1152.46009
author: Peter Šemrl
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-05-15T00:00:00Z
review text: Previously, \textit{T. Oikhberg} and \textit{H. Rosenthal} [Rocky Mt. J. Math. 37, No. 2, 597--608 (2007; Zbl 1138.46006)] proved that if \(d\) is a translation invariant metric on \(X\) such that the multiplication by real scalars is continuous and every one-dimensional subspace of \(X\) is isometric to \(\mathbb R\), then \(d\) is induced by some norm on \(X\). This paper shows that this result can be obtained without a continuity assumption provided that the space is at least two-dimensional.
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46A63
zbMATH DE Number: 5275683
zbMATH Keywords: real normed space
zbMATH Keywords: real linear metric space
zbMATH Keywords: translation invariant metric
reviewed by: Joe Howard
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.01.103
OpenAlex ID: W2002830987
cites work: Sublinear functions on R
cites work: Automorphisms of the Field of Complex Numbers
cites work: Q3218572
cites work: A metric characterization of normed linear spaces
DOI: 10.1016/J.JMAA.2008.01.103
description: scientific article; zbMATH DE number 5275683