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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): Hiroyasu Hamada; Yasuo Watatani
Journal: Proc. Amer. Math. Soc. 138 (2010), 2113-2123.
MSC (2010): Primary 46L55, 47B33; Secondary 37F10, 46L08
Posted: February 9, 2010
MathSciNet review: 2596050
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: Let be a finite Blaschke product of degree at least two with . Then there exists a relation between the associated composition operator on the Hardy space and the -algebra $\mathcal{O}_R (J_R)$ associated with the complex dynamical system $(R^{\circ n})_n$ on the Julia set . We study the -algebra $\mathcal{TC}_R$ generated by both the composition operator and the Toeplitz operator to show that the quotient algebra by the ideal of the compact operators is isomorphic to the -algebra $\mathcal{O}_R (J_R)$ , which is simple and purely infinite.

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