In this paper we investigate the following problem: when a bounded analytic
function ϕ on the unit disk D, fixing 0, is such that {ϕn:n=0,1,2,...} is orthogonal in D?, and consider the
problem of characterizing the univalent, full self-maps of D in
terms of the norm of the composition operator induced. The first problem is
analogous to a celebrated question asked by W. Rudin on the Hardy space setting
that was answered recently ([3] and [15]). The second problem is analogous to a
problem investigated by J. Shapiro in [14] about characterization of inner
functions in the setting of H2.Comment: 8 pages, 1 figure. See also
http://webdelprofesor.ula.ve/nucleotachira/gchacon or
http://webdelprofesor.ula.ve/humanidades/grchaco