  We find a relation between two Hopf algebras built on rooted trees. The first
is the Connes-Kreimer Hopf algebra H_R which describes a certain type of
renormalization in quantum field theory; the second is the Grossman-Larson Hopf
algebra A introduced ten years ago by some "differential" and combinatorial
reasons. Roughly, the relation is the following: there exists a duality between
these two Hopf algebras. We study then two natural operators on A, inspired by
similar ones introduced by Connes and Kreimer for H_R.
