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- W3217781330 abstract "Let $K$ be a compact metric space and let $gamma = (gamma_1, dots, gamma_n)$ be a system of proper contractions on $K$. We study a C*-algebra $mathcal{MC}_{gamma_1, dots, gamma_n}$ generated by all multiplication operators by continuous functions on $K$ and composition operators $C_{gamma_i}$ induced by $gamma_i$ for $i=1, dots, n$ on a certain $L^2$ space. Suppose that $K$ is self-similar. We consider the Hutchinson measure $mu^H$ of $gamma$ and the $L^2$ space $L^2(K, mu^H)$. Then we show that the C*-algebra $mathcal{MC}_{gamma_1, dots, gamma_n}$ is isomorphic to the Cuntz algebra $mathcal{O}_n$ under some conditions." @default.
- W3217781330 created "2021-12-06" @default.
- W3217781330 creator A5003502482 @default.
- W3217781330 date "2021-11-23" @default.
- W3217781330 modified "2023-09-23" @default.
- W3217781330 title "C*-algebras generated by multiplication operators and composition operators with self-similar maps" @default.
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- W3217781330 doi "https://doi.org/10.48550/arxiv.2111.11696" @default.
- W3217781330 hasPublicationYear "2021" @default.
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