Erratum to: Surjective isometries on spaces of vector valued continuous and Lipschitz functions (Positivity, (2013), 17, (395-405), 10.1007/s11117-012-0175-7)


In the original article, the authors claimed incorrectly that the set of extreme points of the unit ball of a subspace A of C(X, F) (X a compact Hausdorff space and F a Banach space) containing the constant functions is equal to {v* ᵒ δx : A → C, v* ϵ ext F*1, x ϵ X}, ext (F*1) denoting the set of extreme points of the unit ball of the dual space F*.We obtain the same conclusion but under some constrains on the range space and on A. More precisely, we assume that the range space is a reflexive Banach space with strictly convex dual and A separates X in the sense of Definition 3.1 in the original article. Strict convexity of the dual implies that F is smooth and then for every unit vector u ϵ F there exits a unique functional u* ϵ F*1 such that u* (u) = 1. Reflexivity implies that every functional is norm attaining. We prove the following result.

Publication Title