### 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 Cr on the Hardy space and the C*-algebra Οr(J_{r}) associated with the complex dynamical system (R^{on})_{n} on the Julia set Jr. We study the C*-algebra τC_{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 Οr(J_{r}), which is simple and purely infinite.

Original language | English |
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Pages (from-to) | 2113-2123 |

Number of pages | 11 |

Journal | Proceedings of the American Mathematical Society |

Volume | 138 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 1 2010 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*138*(6), 2113-2123. https://doi.org/10.1090/S0002-9939-10-10270-6

**Toeplitz-Composition C*-Algebras for certain finite blaschke products.** / Hamada, Hiroyasu; Watatani, Yasuo.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 138, no. 6, pp. 2113-2123. https://doi.org/10.1090/S0002-9939-10-10270-6

}

TY - JOUR

T1 - Toeplitz-Composition C*-Algebras for certain finite blaschke products

AU - Hamada, Hiroyasu

AU - Watatani, Yasuo

PY - 2010/6/1

Y1 - 2010/6/1

N2 - 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 Cr on the Hardy space and the C*-algebra Οr(Jr) associated with the complex dynamical system (Ron)n on the Julia set Jr. We study the C*-algebra τCr generated by both the composition operator Cr and the Toeplitz operator Tz to show that the quotient algebra by the ideal of the compact operators is isomorphic to the C*-algebra Οr(Jr), which is simple and purely infinite.

AB - 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 Cr on the Hardy space and the C*-algebra Οr(Jr) associated with the complex dynamical system (Ron)n on the Julia set Jr. We study the C*-algebra τCr generated by both the composition operator Cr and the Toeplitz operator Tz to show that the quotient algebra by the ideal of the compact operators is isomorphic to the C*-algebra Οr(Jr), which is simple and purely infinite.

UR - http://www.scopus.com/inward/record.url?scp=77951148105&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951148105&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-10-10270-6

DO - 10.1090/S0002-9939-10-10270-6

M3 - Article

VL - 138

SP - 2113

EP - 2123

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 6

ER -