Powers of composition operators: asymptotic behaviour on Bergman, Dirichlet and Bloch spaces. (English) Zbl 1439.30083
Summary: We study the asymptotic behaviour of the powers of a composition operator on various Banach spaces of holomorphic functions on the disc, namely, standard weighted Bergman spaces (finite and infinite order), Bloch space, little Bloch space, Bloch-type space and Dirichlet space. Moreover, we give a complete characterization of those composition operators that are similar to an isometry on these various Banach spaces. We conclude by studying the asymptotic behaviour of semigroups of composition operators on these various Banach spaces.
MSC:
| 30H30 | Bloch spaces |
| 30H99 | Spaces and algebras of analytic functions of one complex variable |
| 47B33 | Linear composition operators |
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