New convexity and fixed point properties in Hardy and Lebesgue-Bochner spaces
type: Item
instance of: scholarly article
title: New convexity and fixed point properties in Hardy and Lebesgue-Bochner spaces
zbMATH Open document ID: 0804.46044
author: V. Pereyra
published in: Journal of Functional Analysis
publication date: 1994-08-22T00:00:00Z
review text: It is shown that for the Hardy class of functions \(H^ 1\) with domain the ball or polydisc in \(\mathbb{C}^ N\), a certain type of uniform convexity property (the uniform Kadec-Klee-Huff property) holds with respect to the topology of pointwise convergence on the interior, which coincides with both the topology of uniform convergence on compacta and the \(\text{weak}^*\) topology on bounded subsets of \(H^ 1\). Also, it is shown that if a Banach space \(X\) has a uniform Kadec-Klee-Huff property, then the Lebesgue-Bochner space \(L_ p(\mu,X)\), \(1\leq p< \infty\), must have a related uniform Kadec-Klee-Huff property. Consequently, by known results, the above spaces have normal structure properties and fixed point properties for non-expansive mappings.
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 599816
zbMATH Keywords: Hardy class
zbMATH Keywords: uniform convexity property
zbMATH Keywords: topology of pointwise convergence on the interior
zbMATH Keywords: uniform Kadec-Klee-Huff property
zbMATH Keywords: Lebesgue- Bochner space
zbMATH Keywords: fixed point properties for non-expansive mappings
MaRDI profile type: Publication
OpenAlex ID: W2003795184
DOI: 10.1006/JFAN.1994.1014
description: scientific article; zbMATH DE number 599816