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Isometries of spaces of unbounded continuous functions

Published online by Cambridge University Press:  17 April 2009

Jesús Araujo  and
Krzysztof Jarosz
Jesús Araujo
Affiliation:
Faculty of Science, University of Cantabria, 39071 Santander, Spain
Krzysztof Jarosz
Affiliation:
Department of Mathematics and Statistics, Southern Illinois University, Edwardsville IL 62026–1653, United States of America
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Abstract

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By the classical Banach-Stone Theorem any surjective isometry between Banach spaces of bounded continuous functions defined on compact sets is given by a homeomorphism of the domains. We prove that the same description applies to isometries of metric spaces of unbounded continuous functions defined on non compact topological spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 3 , June 2001 , pp. 475 - 484
Copyright
Copyright © Australian Mathematical Society 2001

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