On some local geometric properties in Musielak-Orlicz function spaces
type: Item
instance of: scholarly article
title: On some local geometric properties in Musielak-Orlicz function spaces
zbMATH Open document ID: 1078.46018
DOI: 10.4171/ZAA/1216
author: Henryk Hudzik
author: Wojciech Kowalewski
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2005-04-11T00:00:00Z
review text: A point \(x\) in the unit sphere \(S(X)\) of a Banach space \(X\) is a point of compact local uniform rotundity (of the unit ball of \(X\)) if the set \(\{x_n\}\) is a relatively compact set in \(S(X)\) whenever \((x_n)\) is a sequence in \(S(X)\) with \(\| x_n + x \| \rightarrow 2\). In this article, the authors characterize the points of compact local uniform rotundity of the unit ball of Musielak-Orlicz spaces in terms of the Orlicz function generating the space and its conjugate function. The results assume mild restrictions on the Orlicz functions; the measure space is assumed to be nonatomic, complete, and \(\sigma\)-finite; and characterizations are given when the Musielak-Orlicz space is endowed with either the Luxemburg norm or the Orlicz-Amemiya norm. As a corollary, the authors note that, endowed with either norm, a Musielak-Orlicz space is locally uniformly rotund exactly when it is compactly locally uniformly rotund.
reviewed by: B. Turett
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 2155002
zbMATH Keywords: Musielak-Orlicz space
zbMATH Keywords: point of compact local uniform rotundity
MaRDI profile type: Publication
cites work: Uniformly non-l n (1) Musielak-Orlicz Spaces of Bochner Type
cites work: Q4338822
cites work: On the uniform Opial property in some modular sequence spaces
full work available at URL: https://doi.org/10.4171/zaa/1216
OpenAlex ID: W1996936242
description: scientific article; zbMATH DE number 2155002