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

2008/09/18 by Hiroyasu Hamada, Hamada, Hiroyasu, Yasuo Watatani +1
Mathematics · #37F10 #46L08 #46L55 #47B33 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.0809.3061

openalex publication_date 2008/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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