대한수학회지 (Journal of the Korean Mathematical Society)

  • 제45권1호
  • /
  • Pages.197-204
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  • 2008
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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ON DIAMETER PRESERVING LINEAR MAPS

  • 발행 : 2008.01.31
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초록

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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참고문헌

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피인용 문헌

  1. Diameter preserving maps on function spaces vol.21, pp.3, 2017, https://doi.org/10.1007/s11117-016-0438-9
  2. Linear bijections which preserve the diameter of vector-valued maps vol.424, pp.2-3, 2007, https://doi.org/10.1016/j.laa.2007.02.004
  3. Nonlinear Diameter Preserving Maps Between Certain Function Spaces vol.13, pp.6, 2016, https://doi.org/10.1007/s00009-016-0742-4
  4. Nonlinear diameter preserving maps on function spaces pp.1727-933X, 2020, https://doi.org/10.2989/16073606.2018.1536896