Complex extreme points and complex rotundity in Orlicz function spaces equipped with the \(p\)-Amemiya norm
type: Item
instance of: scholarly article
title: Complex extreme points and complex rotundity in Orlicz function spaces equipped with the \(p\)-Amemiya norm
zbMATH Open document ID: 1210.46013
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2010-07-13T00:00:00Z
review text: Necessary and sufficient conditions in order that a point \(x\) of the unit ball \(B(L_{\Phi,p})\) of the complex Orlicz function space \(L_{\Phi,p}\) equipped with the \(p\)-Amemiya norm (\(1\leq p<\infty\)) is a complex extreme point are given. This condition says that \(\mu\{t\in T\colon k\left|x(t)\right|<a_\Phi\}=0\) for any \(k\in K_p(x)\), where \(a_\Phi=\sup\{u\geq 0\colon\Phi(u)=0\}\) and \(K_p (x)\) is the set of all positive numbers \(k\) such that the infimum in the definition of the \(p\)-Amemiya norm of \(x\) is attained at \(k\). As a consequence of this result, it is proved that the space \(L_{\Phi,p}\) is complex strictly convex if and only if \(a_\Phi=0\). Criteria for complex extreme points of \(B(L_{\Phi,\infty})\) and complex strict convexity of the space \(L_{\Phi,\infty}\) are also presented.
reviewed by: Henryk Hudzik
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 5736457
zbMATH Keywords: Orlicz function spaces
zbMATH Keywords: complex extreme points
zbMATH Keywords: complex strict convexity
zbMATH Keywords: \(p\)-Amemiya norm
author: Li-Li Chen
author: Yunan Cui
MaRDI profile type: Publication
full work available at URL: j.na.2010.04.071
OpenAlex ID: W2011930663
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DOI: 10.1016/J.NA.2010.04.071
description: scientific article; zbMATH DE number 5736457