Bulletin of the Belgian Mathematical Society - Simon Stevin

Realcompactness and Banach-Stone theorems

Jesús Araujo

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Abstract

For realcompact spaces $X$ and $Y$ we give a complete description of the linear biseparating maps between spaces of vector-valued continuous functions on $X$ and $Y$ in two cases: the spaces of all continuous functions and the spaces of {\em bounded} continuous functions. With similar techniques we also describe the linear biseparating maps defined between some other families of spaces, in particular spaces of vector-valued uniformly continuous bounded functions.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 11, Number 2 (2004), 247-258.

Dates
First available in Project Euclid: 11 June 2004

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1086969315

Digital Object Identifier
doi:10.36045/bbms/1086969315

Mathematical Reviews number (MathSciNet)
MR2080425

Zentralblatt MATH identifier
1077.46029

Subjects
Primary: 46E40: Spaces of vector- and operator-valued functions
Secondary: 47B33: Composition operators 47B38: Operators on function spaces (general) 54D60: Realcompactness and realcompactification

Keywords
Biseparating map Banach-Stone theorem realcompact space spaces of countinuous functions spaces of uniformly continuous functions

Citation

Araujo, Jesús. Realcompactness and Banach-Stone theorems. Bull. Belg. Math. Soc. Simon Stevin 11 (2004), no. 2, 247--258. doi:10.36045/bbms/1086969315. https://projecteuclid.org/euclid.bbms/1086969315


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