Extremal structure of the unit ball of \(L^ p(\mu,X)\)
type: Item
instance of: scholarly article
title: Extremal structure of the unit ball of \(L^ p(\mu,X)\)
zbMATH Open document ID: 0877.46020
author: Zhibao Hu
author: Bor-Luh Lin
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-12-08T00:00:00Z
review text: The authors consider and investigate a subset \(K\) of a real Banach space \(X\) and an extreme point \((\text{ext }K)\), a strongly extreme point \((\text{str-ext }K)\), an exposed point of \(K\), a strongly exposed point of \(K\) and they also a weak\(^*\) exposed point of \(K\) and a weak\(^*\) strongly exposed point of \(K\), and also consider the spaces \(L^q(\mu,X^*)\), \(L^p(\mu,X)\), \(L^p(\mu,X)^*\), \(L^q(\mu_{f,q},X^*)\), \(B_{L^p(\mu,X)^*}\), \(S_{L^q(\mu,X^*)}\). This long and important paper contains 15 theorems in which there are given e.g. properties of weak\(^*\) strongly exposed points, weak\(^*\) exposed points and also representations of the dual space \(L^p(\mu,X)\) as spaces of certain weak\(^*\) measurable functions from \(\Omega\) to \(X^*\).
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 908592
zbMATH Keywords: spaces of measurable functions
zbMATH Keywords: extreme point
zbMATH Keywords: strongly extreme point
zbMATH Keywords: exposed point
zbMATH Keywords: strongly exposed point
zbMATH Keywords: weak\(^*\) strongly exposed point
zbMATH Keywords: representations of the dual space
reviewed by: Aleksander Waszak
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0225
OpenAlex ID: W2080959904
DOI: 10.1006/JMAA.1996.0225
description: scientific article; zbMATH DE number 908592