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.
Publié le : 2004-06-14
Classification:
Biseparating map,
Banach-Stone theorem,
realcompact space,
spaces of countinuous functions,
spaces of uniformly continuous functions,
46E40,
47B33,
47B38,
54D60
@article{1086969315,
author = {Araujo, Jes\'us},
title = {Realcompactness and Banach-Stone theorems},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {11},
number = {1},
year = {2004},
pages = { 247-258},
language = {en},
url = {http://dml.mathdoc.fr/item/1086969315}
}
Araujo, Jesús. Realcompactness and Banach-Stone theorems. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2004) no. 1, pp. 247-258. http://gdmltest.u-ga.fr/item/1086969315/