Diameter preserving linear bijections and \({\mathcal C}_0(L)\) spaces (Q983867)

Let \(X,Y\) be infinite compact sets and let \(L\) be a locally compact set such that the dual unit ball of \(C_0(L)\) is the norm closed convex hull of its extreme points. For any Banach space \(V\), consider the space of continuous functions, \(C(X,V)\). In this paper the authors give a complete description of a diameter preserving linear bijection \(T: C(X,V) \to C(Y,C_0(L))\) in terms of \(t: L \to \text{hom}(Y,X)\) that is continuous for the topology of pointwise convergence, a linear map \(\alpha:C(X,V) \to C_0(L)\) and an onto isometry \(G:V \to C_0(L)\).