Discontinuous maps from Lipschitz algebras
type: Item
instance of: scholarly article
title: Discontinuous maps from Lipschitz algebras
zbMATH Open document ID: 0913.46045
author: B. Pavlović
published in: Journal of Functional Analysis
publication date: 1999-05-20T00:00:00Z
review text: The existence of homomorphisms and derivations from the little Lipschitz algebra lip\(_\alpha(X)=\{f\in\) Lip\(_\alpha(X): | f(t)-f(s)| /d(t,s)^\alpha\to 0\) as \(d(t,s)\to 0\}\subset \) Lip\(_\alpha(X)\), \(0<\alpha<1\), on an infinite compact metric space \(X\), that are discontinuous on every dense subalgebra is established in this article. As a corollary it is shown that given a \(\beta\in[\alpha,\) min\(\{2\alpha,1\})\) there are homomorphisms and derivations that are discontinuous with respect to the Lipschitz norm on lip\(_\delta(X)\) for all \(\delta\in[\alpha, \beta]\). The article is a continuation of a previous paper by the same author.
Mathematics Subject Classification ID: 46J10
zbMATH DE Number: 1199817
zbMATH Keywords: little Lipschitz algebra
zbMATH Keywords: homomorphism
zbMATH Keywords: derivation
zbMATH Keywords: linear functional
zbMATH Keywords: eventual continuity
reviewed by: Thomas V. Tonev
MaRDI profile type: Publication
full work available at URL: jfan.1997.3232
OpenAlex ID: W2021393889
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DOI: 10.1006/JFAN.1997.3232
description: scientific article; zbMATH DE number 1199817