Abstract
Let \(\lambda _i (i=1,\ldots ,k)\) be nonzero complex scalars and \(\varphi _i (i=1,..,k)\) be analytic self-maps of the unit disk \(\mathbb {D}\). We show that the operator \(\sum _{i=1}^k\lambda _iC_{\varphi _i}\) is compact on the Bloch space \(\mathcal {B}\) if and only if
We also study the linear combination of composition operators on the Banach algebra of bounded analytic functions.
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This project was partially supported by NNSF of China (No. 11471143 and No. 11720101003) and the Macao Science and Technology Development Fund (No. 186/2017/A3).
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Shi, Y., Li, S. Linear combination of composition operators on \(H^\infty \) and the Bloch space. Arch. Math. 112, 511–519 (2019). https://doi.org/10.1007/s00013-019-01307-8
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DOI: https://doi.org/10.1007/s00013-019-01307-8