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- 저자 : Antonio Aizpuru (검색결과 2 건)
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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.
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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.
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