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On diameter preserving linear maps
Antonio Aizpuru,Montserrat Tamayo 대한수학회 2008 대한수학회지 Vol.45 No.1
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. 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.
ON DIAMETER PRESERVING LINEAR MAPS
Aizpuru, Antonio,Tamayo, Montserrat Korean Mathematical Society 2008 대한수학회지 Vol.45 No.1
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.