Journal of Operator Theory

Volume 55, Issue 2, Spring 2006 pp. 285-294.

The noncompact Banach-Stone theorem

Authors: Jes\'us Araujo
Author institution: Departamento de Matem\'aticas, Estadistica y Computaci\'on, Facultad de Ciencias, Universidad de Cantabria, Avenida de los Castros s.n., E-39071, Santander, Spain

Summary: We give a complete description of the linear isometries between spaces of vector-valued bounded continuous functions defined on some natural families of topological spaces which may be neither compact nor locally compact. A similar study is carried out for spaces of vector-valued bounded uniformly continuous functions.

Keywords: Banach-Stone theorem, linear isometry, biseparating map, disjointness preserving, realcompact space, vector-valued bounded functions.

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