• Title/Summary/Keyword: diameter preserving map

Search Result 1, Processing Time 0.015 seconds

ON DIAMETER PRESERVING LINEAR MAPS

  • Aizpuru, Antonio;Tamayo, Montserrat
    • Journal of the Korean Mathematical Society
    • /
    • v.45 no.1
    • /
    • pp.197-204
    • /
    • 2008
  • 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.