## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

### Realcompactness and Banach-Stone theorems

#### 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