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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