We characterize those analytic self-maps <p of the unit disc which generate bounded or compact composition operators Cv between given weighted Banach spaces H£° or H® 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. 1991 Mathematics subject classification (Amer. Math. Soc): ...

We study the boundedness and compactness of the differences of two weighted composition operators acting from the Bloch space B to the space H∞ of bounded analytic functions on the open unit disk. Such a study has a relationship to the topological structure problem of composition operators on H∞. Using this relation, we will estimate the operator norms and the essential norms of the differences...

In this paper the complete solution of the restricted inequalities for supremal operators are given. The boundedness of the composition of supremal operators with the Hardy and Copson operators in weighted Lebesgue spaces are characterized.