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We characterize the boundedness and compactness of weighted composition operators between weighted Banach spaces of analytic functions //° and H£°. We estimate the essential norm of a weighted composition operator and compute it for those Banach spaces W° which are isomorphic to CQ. We also show that, when such an operator is not compact, it is an isomorphism on a subspace isomorphic to c 0 or looFinally, we apply these results to study composition operators between Bloch type spaces and little Bloch type spaces.2000 Mathematics subject classification: primary 47B38; secondary 30D45,46E15.

Efficiency has become one of the main concerns in evolutionary multiobjective optimization during recent years. One of the possible alternatives to achieve a faster convergence is to use a relaxed form of Pareto dominance that allows us to regulate the granularity of the approximation of the Pareto front that we wish to achieve. One such relaxed forms of Pareto dominance that has become popular in the last few years is ε-dominance, which has been mainly used as an archiving strategy in some multiobjective evolutionary algorithms. Despite its advantages, ε-dominance has some limitations. In this paper, we propose a mechanism that can be seen as a variant of ε-dominance, which we call Pareto-adaptive ε-dominance (paε-dominance). Our proposed approach tries to overcome the main limitation of ε-dominance: the loss of several nondominated solutions from the hypergrid adopted in the archive because of the way in which solutions are selected within each box.

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Ž .Let , be analytic functions defined on ‫,ބ‬ such that ‫ބ‬ : ‫.ބ‬ The operator Ž . given by f ¬ f ( is called a weighted composition operator. In this paper we deal with the boundedness, compactness, weak compactness, and complete continu-Ž . ity of weighted composition operators on Hardy spaces H 1 F p -ϱ . In p particular, we prove that such an operator is compact on H if and only if it is 1 weakly compact on this space. This result depends on a technique which passes the weak compactness from an operator T to operators dominated in norm by T.