  We consider semicrossed products of the disk algebra with respect to
endomorphisms defined by finite Blaschke products. We characterize the Jacobson
radical of these operator algebras. Furthermore, in the case the finite
Blaschke product is elliptic, we show that the semicrossed product contains no
nonzero quasinilpotent elements. However, if the finite Blaschke product is
hyperbolic or parabolic with zero hyperbolic step, the Jacobson radical is
nonzero and a proper subset of the set of quasinilpotent elements.
