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ON DIAMETER PRESERVING LINEAR MAPS
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 Title & Authors
ON DIAMETER PRESERVING LINEAR MAPS
Aizpuru, Antonio; Tamayo, Montserrat;
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 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 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;
 Language
English
 Cited by
3time(s) in CrossRef
1.
Diameter preserving maps on function spaces, Positivity, 2016  crossref(new windwow)
2.
Linear bijections which preserve the diameter of vector-valued maps, Linear Algebra and its Applications, 2007, 424, 2-3, 371  crossref(new windwow)
3.
Nonlinear Diameter Preserving Maps Between Certain Function Spaces, Mediterranean Journal of Mathematics, 2016, 13, 6, 4237  crossref(new windwow)
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