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Composition operators between weighted Banach spaces of analytic functions. (English) Zbl 0912.47014
Summary: We characterize those analytic self-maps \(\varphi\) of the unit disc which generate bounded or compact composition operators \(C_\varphi\) between given weighted Banach spaces \(H^\infty_v\) or \(H^0_v\) of analytic functions with the weighted sup-norms. We characterize also those composition operators which are bounded or compact with respect to all reasonable weights \(v\).

MSC:
47B38 Linear operators on function spaces (general)
30D55 \(H^p\)-classes (MSC2000)
46E15 Banach spaces of continuous, differentiable or analytic functions
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