# C*-algebras generated by multiplication operators and composition operators by functions with self-similar branches

@article{Hamada2019CalgebrasGB, title={C*-algebras generated by multiplication operators and composition operators by functions with self-similar branches}, author={Hiroyasu Hamada}, journal={arXiv: Operator Algebras}, year={2019} }

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…

## One Citation

C*-algebras generated by multiplication operators and composition operators with self-similar maps

- Mathematics
- 2021

Abstract. Let K be a compact metric space and let γ = (γ1, . . . , γn) be a system of proper contractions on K. We study a C∗-algebra MCγ1,...,γn generated by all multiplication operators by…

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