In this paper we are concerned
with the problem, posed by R. R. Phelps, of describing the into isometries of
the disk algebra. We show that, in a certain sense, every isometry can be
approximated by convex combinations of isometries of the form f → k(f ∘ ϕ).
We also give some sufficient conditions for an isometry to be of the form
f → k(f ∘ ϕ).