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http://dx.doi.org/10.4134/JKMS.2008.45.1.197

ON DIAMETER PRESERVING LINEAR MAPS  

Aizpuru, Antonio (Departmento de Matematicas Universidad de Cadiz)
Tamayo, Montserrat (Department de Matematicas Universidad de Cadiz)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.1, 2008 , pp. 197-204 More about this Journal
Abstract
We study diameter preserving linear maps from C(X) into C(Y) where X and Y are compact Hausdorff spaces. By using the extreme points of $C(X)^*\;and\;C(Y)^*$ and a linear condition on them, we obtain that there exists a diameter preserving linear map from C(X) into C(Y) if and only if X is homeomorphic to a subspace of Y. We also consider the case when X and Y are noncompact but locally compact spaces.
Keywords
diameter preserving map; extreme point; locally compact space;
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