Toeplitz-composition C*-algebras for certain finite Blaschke products

Details Toeplitz-composition C*-algebras for certain finite Blaschke products Toeplitz-composition C*-algebras for certain finite Blaschke products

2008-09-18

arxiv.org/abs/0809.3061v1

Mathematics

Operator Algebras

14 pages

Scientific paper

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 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.

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