How does the distortion of linear embedding of \(C_0(K)\) into \(C_0(\Gamma ,X)\) spaces depend on the height of \(K\)?
type: Item
instance of: scholarly article
title: How does the distortion of linear embedding of \(C_0(K)\) into \(C_0(\Gamma ,X)\) spaces depend on the height of \(K\)?
zbMATH Open document ID: 1271.46006
author: Leandro Candido
author: Elói M. Galego
published in: Journal of Mathematical Analysis and Applications
publication date: 2013-04-22T00:00:00Z
review text: The authors consider the classical questions of the `Banach-Stone' type for the space of vector-valued continuous functions \(C(K, X)\), when the Banach space \(X\) has non-trivial cotype. It is shown that for an infinite discrete set \(\Gamma\) and a locally compact space \(K\), if there is an into isomorphism \(T: C_0(K) \rightarrow C_0(\Gamma, X)\), then \(K\) has finite height and \(\|T^{-1}\|\|T\| \geq 2 ht(K)-1\). See also [the authors, Fundam. Math. 220, No. 1, 83--92 (2013; Zbl 1271.46005)] for related results.
reviewed by: T.S.S.R.K. Rao
Mathematics Subject Classification ID: 46B03
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 6156113
zbMATH Keywords: spaces of vector-valued continuous functions
zbMATH Keywords: bounds for isomorphisms
zbMATH Keywords: height of locally compact scattered space
MaRDI profile type: Publication
full work available at URL: j.jmaa.2013.01.017
OpenAlex ID: W2745418410
DOI: 10.1016/J.JMAA.2013.01.017
description: scientific article; zbMATH DE number 6156113