Biseparating maps and homeomorphic real-compactifications
type: Item
instance of: scholarly article
title: Biseparating maps and homeomorphic real-compactifications
zbMATH Open document ID: 0828.47024
author: Jesús Araujo
author: Edward Beckenstein
author: Lawrence Narici
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-01-08T00:00:00Z
review text: If \(X\) and \(Y\) are realcompact and \(T : C(X) \to C(Y)\) is a ring isomorphism then two things happen: (1) there is a homeomorphism \(h\) of \(X\) onto \(Y\) and (2) \(T\) is a composition map: for all \(f\) in \(C(X)\), \(Tf = f \circ h\). The authors strengthen that result. They discard the multiplicative property of \(T\) and assume only that \(T\) is biseparating in the sense that \(fg = 0 \Leftrightarrow Tf Tg = 0\). It remains true that \(X\) is homeomorphic to \(Y\) but this time, if \(T\) is also linear, it is a weighted composition map: for some weight function \(a\) in \(C(Y)\), \(Tf = a(f \circ h)\).
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 46E10
zbMATH DE Number: 786129
zbMATH Keywords: homeomorphism
zbMATH Keywords: composition map
zbMATH Keywords: biseparating
zbMATH Keywords: weighted composition map
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1170
OpenAlex ID: W2073940614
DOI: 10.1006/JMAA.1995.1170
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description: scientific article; zbMATH DE number 786129