Linear bijections which preserve the diameter of vector-valued maps Original Research Article

We study diameter preserving linear bijections from image onto image, where X,Y are compact Hausdorff spaces and V, Z are Banach spaces. In particular, assuming that Z is rotund and the extreme points of BV* satisfy a certain geometric condition, we prove that there exists a diameter preserving linear bijection from image onto image if and only if X is homeomorphic to Y and Z is linearly isometric to V. We also consider the case when X and Y are locally compact, noncompact spaces.