Minimal topologies and \(L_p\)-spaces
type: Item
instance of: scholarly article
title: Minimal topologies and \(L_p\)-spaces
zbMATH Open document ID: 0403.46008
published in: Illinois Journal of Mathematics
publication date: 1980-01-01T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ijm/1256047804
review text: This paper deals with minimal topologies on Riesz spaces. A minimal topology is a Hausdorff locally solid topology that is coarser than any other Hausdorff locally solid topology on the space. It is shown that every minimal topology satisfies the Lebesgue property, that an Archimedean Riesz space can admit a locally convex-solid topology that is minimal if and only if the space is discrete, that \(C[0,1]\) and \(L_\infty([0,1])\) do not admit a minimal topology, and that the topology of convergence in measure on \(L_p([0,1])\) \((0<p<\infty)\) is a minimal topology. A similar result is shown for certain Orlicz spaces.
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 3626030
zbMATH Keywords: minimal topologies
zbMATH Keywords: Riesz spaces
zbMATH Keywords: locally solid topology
zbMATH Keywords: Lebesgue property
zbMATH Keywords: topology of convergence in measure
zbMATH Keywords: Orlicz spaces
author: Charalambos D. Aliprantis
author: Owen Burkinshaw
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3626030