On the distortion of a linear embedding of \(C(K)\) into a \(C_{0}(\varGamma,X)\) space
type: Item
instance of: scholarly article
title: On the distortion of a linear embedding of \(C(K)\) into a \(C_{0}(\varGamma,X)\) space
zbMATH Open document ID: 1383.46020
author: Leandro Candido
published in: Journal of Mathematical Analysis and Applications
publication date: 2017-12-12T00:00:00Z
review text: The distortion \(\| T\| \| T^{-1}\|\) of a linear embedding \(T: C(K) \to C_{0}(\Gamma, X)\) is studied, where \(K\) is a compact Hausdorff space, \(\Gamma\) is an infinite discrete topological space and \(X\) is a Banach space. The author proves that, if \(X\) contains no subspace isomorphic to \(c_{0}\) and, for some positive integer \(n\), the \(n\)th derivative of \(K\) is non-empty, then \(\| T\| \| T^{-1}\| \geq 2n+1\). This theorem extends a result of \textit{L. Candido} and \textit{E. M. Galego} [Fundam. Math. 218, No. 2, 151--163 (2012; Zbl 1258.46002)] and answers a question from [\textit{L. Candido} and \textit{E. M. Galego}, J. Math. Anal. Appl. 402, No. 1, 185--190 (2013; Zbl 1271.46006)].
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 46E40
zbMATH DE Number: 6817625
zbMATH Keywords: \(C_{0}(K, X)\) spaces
zbMATH Keywords: \(C(K)\) spaces
zbMATH Keywords: linear embeddings
zbMATH Keywords: Banach-Mazur distances
reviewed by: Elói M. Galego
MaRDI profile type: Publication
full work available at URL: j.jmaa.2017.11.039
OpenAlex ID: W2768773788
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DOI: 10.1016/J.JMAA.2017.11.039
description: scientific article; zbMATH DE number 6817625