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): ...

In present paper a certain convolution operator of analytic functions is defined. Moreover, subordination and superordination- preserving properties for a class of analytic operators defined on the space of normalized analytic functions in the open unit disk is obtained. We also apply this to obtain sandwich results and generalizations of some known results.