On Musielak-Orlicz spaces isometric to \(L_2\) or \(L \infty\)
type: Item
instance of: scholarly article
title: On Musielak-Orlicz spaces isometric to \(L_2\) or \(L \infty\)
zbMATH Open document ID: 0892.46027
published in: Collectanea Mathematica
publication date: 1997-09-15T00:00:00Z
full work available at URL: https://eudml.org/doc/40806
review text: It is proved that a Musiełak-Orlicz space \(L_\Phi\) of real valued functions which is isometric to a Hilbert space coincides with \(L_2\) up to a weight, that is \(\Phi(u,t)= c(t)u^2\). Moreover, it is shown that any surjective isometry between \(L_\Phi\) and \(L_\infty\) is a weighted composition operator and a criterion for \(L_\Phi\) to be isometric to \(L_\infty\) is presented.
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 1060663
zbMATH Keywords: Musiełak-Orlicz
zbMATH Keywords: surjective isometry
zbMATH Keywords: weighted composition operator
author: Anna Kamińska
reviewed by: Anna Kamińska
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1060663