Approximation of *weak-to-norm continuous mappings
泛函分析
2007-05-23 v1 经典分析与常微分方程
摘要
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.
引用
@article{arxiv.math/0007124,
title = {Approximation of *weak-to-norm continuous mappings},
author = {Lorenzo D'Ambrosio},
journal= {arXiv preprint arXiv:math/0007124},
year = {2007}
}
备注
13 pages