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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.

The use of the Internet to develop new technologies has generated a considerable change in teaching and student learning in higher education. The pandemic caused by COVID-19 has forced universities to switch from face-to-face to online instruction. Furthermore, this transfer process was planned and executed quickly, with urgent redesigns of courses originally conceived for live teaching. The aim of this work is to measure the service quality of online teaching delivered during the COVID-19 period. The methodology was based on an importance-performance analysis using a structural equations model. The data were obtained from a sample of 467 students attending a university in southern Spain. The results reveal five priority attributes of online teaching that need to be improved in order to enhance the service quality of the virtual instruction provided to students. Universities need to redefine their online format by integrating methodological and technological decisions and involving collaboration between teachers, students and administration staff and services. The results do not apply to educational institutions that exclusively teach courses online, but to those institutions that had to rapidly adapt, and shift course material originally designed for face-to-face training.

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