Fixed point properties in Hardy spaces
type: Item
instance of: scholarly article
title: Fixed point properties in Hardy spaces
zbMATH Open document ID: 1205.47049
author: Narcisse Randrianantoanina
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-08-11T00:00:00Z
review text: The author proves that \(H^1(\Delta)\) has the weak* fixed point property for left reversible semigroups, where \(\Delta \) denotes the open unit disc of \(\mathbb C\) and \[ H^p(\Delta)=\{f:\Delta \to\mathbb C\text{ holomorphic}:\|f\|_{H^p(\Delta)}<\infty\}, \] \(0<p\leq \infty\), is the Hardy space on \(\Delta\). Also, it is investigated the case of higher dimensions, the case of Hardy spaces on the polydisc, and then it is explained how the case of more general domains such as Euclidian balls can be treated with a similar approach.
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 5768924
zbMATH Keywords: fixed point property
zbMATH Keywords: left reversible semigroup
zbMATH Keywords: Hardy space
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.04.023
OpenAlex ID: W2039373502
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DOI: 10.1016/J.JMAA.2010.04.023
description: scientific article; zbMATH DE number 5768924