%0 Journal Article
%A Gallardo Gutiérrez, Eva Antonia
%A González, María J.
%T Exceptional sets and Hilbert–Schmidt composition operators
%D 2003
%@ 0022-1236
%U https://hdl.handle.net/20.500.14352/58436
%X It is shown that an analytic map phi of the unit disk into itself inducing a Hilbert-Schmidt composition operator on the Dirichlet space has the property that the set E-phi = {e(i0)is an element ofpartial derivativeD : \phi(e(10))\ = 1 has zero logarithmic capacity. We also show that this is no longer true for compact composition operators on the Dirichlet space. Moreover, such a condition is not even satisfied by Hilbert-Schmidt composition operators on the Hardy space.
%~