Surjective isometries on a Banach space of analytic functions on the open unit disc (Q2420838)

Let \({\mathcal D}\) be the unit disc. Let \(S_A\) denote the space of analytic functions whose derivative has a continuous extension to the closed unit disc, equipped with the norm \(\|f\|= |f(0)|+ \sup\{|f'(z)|: z \in {\mathcal D}\}\). Let \(T: S_A \rightarrow S_A\) be a surjective isometry (not necessarily linear). After applying the Mazur-Ulam theorem in the real scalars, the authors give a description of \(T-T(0)\).