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arXiv · 1502.02093

C*-algebras generated by multiplication operators and composition operators with rational symbol

Hiroyasu Hamada
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Abstract

Let $R$ be a rational function of degree at least two, let $J_R$ be the Julia set of $R$ and let $μ^L$ be the Lyubich measure of $R$. We study the C$^*$-algebra $\mathcal{MC}_R$ generated by all multiplication operators by continuous functions in $C(J_R)$ and the composition operator $C_R$ induced by $R$ on $L^2(J_R, μ^L)$. We show that the C$^*$-algebra $\mathcal{MC}_R$ is isomorphic to the C$^*$-algebra $\mathcal{O}_R (J_R)$ associated with the complex dynamical system $\{R^{\circ n} \}_{n=1} ^\infty$.

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Hiroyasu Hamada. 2015-02-07. C*-algebras generated by multiplication operators and composition operators with rational symbol. https://arxiv.org/abs/1502.02093

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