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- W4288019700 abstract "Let $K$ be a compact metric space and let $varphi: K to K$ be continuous. We study C*-algebra $mathcal{MC}_varphi$ generated by all multiplication operators by continuous functions on $K$ and a composition operator $C_varphi$ induced by $varphi$ on a certain $L^2$ space. Let $gamma = (gamma_1, dots, gamma_n)$ be a system of proper contractions on $K$. Suppose that $gamma_1, dots, gamma_n$ are inverse branches of $varphi$ and $K$ 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 $mathcal{MC}_varphi$ is isomorphic to the C*-algebra $mathcal{O}_gamma (K)$ associated with $gamma$ under some conditions." @default.
- W4288019700 created "2022-07-26" @default.
- W4288019700 creator A5029283210 @default.
- W4288019700 date "2019-11-22" @default.
- W4288019700 modified "2023-09-30" @default.
- W4288019700 title "C*-algebras generated by multiplication operators and composition operators by functions with self-similar branches" @default.
- W4288019700 doi "https://doi.org/10.48550/arxiv.1911.10993" @default.
- W4288019700 hasPublicationYear "2019" @default.
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