Abstract
In this paper, we study properties of the topological space of composition operators acting on the space \({\mathcal{H}^{\infty}}\) of Dirichlet series. Especially, we show that there are two compact composition operators which are not in the same path component on \({\mathcal{H}^{\infty}}\). This is in sharp contrast with the classical case where all compact composition operators on \({H^{\infty}}\) of one variable or several variables lie in the same path component.
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This work is supported by the National Natural Science Foundation of China (Grant Nos. 11271293, 11431011, 11471251).
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Wang, M., Yao, X. Topological structure of the space of composition operators on \({\mathcal{H}^{\infty}}\) of Dirichlet series. Arch. Math. 106, 471–483 (2016). https://doi.org/10.1007/s00013-016-0897-z
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DOI: https://doi.org/10.1007/s00013-016-0897-z