Journal of the
Korean Mathematical Society JKMS

We study diameter preserving linear maps from $C(\mathrm{X})$ into $C(\mathrm{Y})$ where $\mathrm{X}$ and $\mathrm{Y}$ are compact Hausdorff spaces. By using the extreme points of $C(\mathrm{X})^{*}$ and $C(\mathrm{Y})^{*}$ and a linear condition on them, we obtain that there exists a diameter preserving linear map from $C(\mathrm{X})$ into $C(\mathrm{Y})$ if and only if $\mathrm{X}$ is homeomorphic to a subspace of $\mathrm{Y}$. We also consider the case when $\mathrm{X}$ and $\mathrm{Y}$ are noncompact but locally compact spaces.

Keywords: diameter preserving map, extreme point, locally compact space

MSC numbers: Primary 47B38; Secondary 54D45