Diameter preserving linear bijections and \({\mathcal C}_0(L)\) spaces
type: Item
instance of: scholarly article
title: Diameter preserving linear bijections and \({\mathcal C}_0(L)\) spaces
zbMATH Open document ID: 1206.46013
author: F. Rambla
author: A. Aizpuru
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2010-07-13T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1274896212
review text: Let \(X,Y\) be infinite compact sets and let \(L\) be a locally compact set such that the dual unit ball of \(C_0(L)\) is the norm closed convex hull of its extreme points. For any Banach space \(V\), consider the space of continuous functions, \(C(X,V)\). In this paper the authors give a complete description of a diameter preserving linear bijection \(T: C(X,V) \to C(Y,C_0(L))\) in terms of \(t: L \to \text{hom}(Y,X)\) that is continuous for the topology of pointwise convergence, a linear map \(\alpha:C(X,V) \to C_0(L)\) and an onto isometry \(G:V \to C_0(L)\).
Mathematics Subject Classification ID: 46B04
Mathematics Subject Classification ID: 46B25
Mathematics Subject Classification ID: 46E40
zbMATH DE Number: 5735941
zbMATH Keywords: diameter preserving linear maps
zbMATH Keywords: spaces of vector-valued continuous functions
zbMATH Keywords: Banach-Stone theorem
reviewed by: T.S.S.R.K. Rao
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5735941