ON DIAMETER PRESERVING LINEAR MAPS

Title & Authors
ON DIAMETER PRESERVING LINEAR MAPS
Aizpuru, Antonio; Tamayo, Montserrat;

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 $\small{C(X)^*\;and\;C(Y)^*}$ 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;
Language
English
Cited by
1.
Diameter preserving maps on function spaces, Positivity, 2017, 21, 3, 875
2.
Linear bijections which preserve the diameter of vector-valued maps, Linear Algebra and its Applications, 2007, 424, 2-3, 371
3.
Nonlinear Diameter Preserving Maps Between Certain Function Spaces, Mediterranean Journal of Mathematics, 2016, 13, 6, 4237
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