Linear isometries between real Banach algebras of continuous complex-valued functions
type: Item
instance of: scholarly article
title: Linear isometries between real Banach algebras of continuous complex-valued functions
zbMATH Open document ID: 1307.46040
DOI: 10.1155/2013/506129
author: Davood Alimohammadi
author: Hadis Pazandeh
published in: Journal of Operators
publication date: 2014-11-19T00:00:00Z
review text: Summary: Let \(X\) and \(Y\) be compact Hausdorff spaces, and let \(\tau\) and \(\eta\) be topological involutions on \(X\) and \(Y\), respectively. In [Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 30, No. 2, 343--356 (1991; Zbl 0764.46051)], \textit{S. H. Kulkarni} and \textit{S. Arundhathi} characterized linear isometries from a real uniform function algebra \(A\) on \((X,\tau)\) onto a real uniform function algebra \(B\) on \((Y,\eta)\) applying their Choquet boundaries and showed that these mappings are weighted composition operators. In this paper, we characterize all onto linear isometries and certain into linear isometries between \(C(X,\tau)\) and \(C(Y,\eta)\) applying the extreme points in the unit balls of \(C(X,\tau)^*\) and \(C(Y,\eta)^*\).
Mathematics Subject Classification ID: 46J10
Mathematics Subject Classification ID: 47B48
Mathematics Subject Classification ID: 46B04
zbMATH DE Number: 6371130
zbMATH Keywords: Banach-Stone-theorem
zbMATH Keywords: isometries
zbMATH Keywords: function algebra
zbMATH Keywords: weighted composition operators
Wikidata QID: Q59020445
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/506129
OpenAlex ID: W1969536442
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description: scientific article; zbMATH DE number 6371130