Order completeness in Lipschitz algebras
type: Item
instance of: scholarly article
title: Order completeness in Lipschitz algebras
zbMATH Open document ID: 0922.46022
published in: Journal of Functional Analysis
publication date: 1999-10-14T00:00:00Z
review text: The algebraic properties of Lipschitz algebras, including complex homomorphisms and ideals, have been well understood in the case when the underlying metric space is compact. It was earlier shown by the author of the reviewed paper in [Pac. J. Math. 164, No. 1, 179-193 (1994; Zbl 0797.46007)] that Lipschitz algebras are order-complete. Assuming the hypothesis of order continuity (or order closure) in place of norm continuity, the author obtains a characterization of order-continuous complex homomorphisms and order-complete subalgebras, without the usual restriction of compactness of the underlying metric space. As a corollary, it is shown that order-complete subalgebras and quotients of Lipschitz spaces by order-complete ideals are also Lipschitz spaces.
Mathematics Subject Classification ID: 46E25
Mathematics Subject Classification ID: 46E05
zbMATH DE Number: 764041
zbMATH Keywords: Lipschitz algebras
zbMATH Keywords: complex homomorphisms
zbMATH Keywords: ideals
zbMATH Keywords: order continuity
zbMATH Keywords: order closure
zbMATH Keywords: order completeness
author: Nik Weaver
reviewed by: Mikhail Tkachenko
MaRDI profile type: Publication
full work available at URL: jfan.1995.1065
OpenAlex ID: W1965297651
DOI: 10.1006/JFAN.1995.1065
description: scientific article; zbMATH DE number 764041