Endomorphisms of the riordan group, some new facts

Abstract

We consider endomorphisms of the Riordan group. This issue was recently studied by Petrullo and Senato who gave the characterization of these endomorphisms in terms of endomorphisms of the Appell and the Associated subgroup. Here, we show that some of the latter ones turn out to be identities. Additionally, we establish some facts concerning the action of these endomorphism on the diagonal Riordan arrays.