Toeplitz-composition $C^{*}$-algebras for certain finite Blaschke products

Hiroyasu Hamada, Yasuo Watatani
2010 Proceedings of the American Mathematical Society  
Let 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 O R (J R ) associated with the complex dynamical system (R •n ) n on the Julia set J R . We study the C * -algebra T C R 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 O R (J R ), which is simple and purely infinite.
doi:10.1090/s0002-9939-10-10270-6 fatcat:227l36c5zzen3bjhhc5lewu7ma