2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169384Let R be a finite Blaschke product of degree at least two with R(0)=0. Then there exists a relation between the associated composition operator C_R on the Hardy space and the C*-algebra associated with the complex dynamical system on the Julia set of R. We study the C*-algebra generated by both the composition operator C_R and the Toeplitz operator T_z to show that the quotient algebra by the ideal of the compact operators is isomorphic to the C*-algebra associated with the complex dynamical system, which is simple and purely infinite.14 pagesOperator AlgebrasFunctional Analysis46L55, 47B33, 37F10, 46L08text