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Approximation of *weak-to-norm continuous mappings

Lorenzo D'Ambrosio
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Abstract

The purpose of this paper is to study the approximation of vector valued mappings defined on a subset of a normed space. We investigate Korovkin-type conditions under which a given sequence of linear operators becomes a so-called approximation process. First, we give a sufficient condition for this sequence to approximate the class of bounded, uniformly continuous functions. Then we present some sufficient and necessary conditions guaranteeing the approximation within the class of unbounded, *weak-to-norm continuous mappings. We also derive some estimates of the rate of convergence.

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Lorenzo D'Ambrosio. 2000-07-20. Approximation of *weak-to-norm continuous mappings. https://doi.org/10.1006/jath.2002.3708

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