Korovkin theory for cone-valued functions

被引：0

作者：

Walter Roth

机构：

[1] Universiti Brunei Darussalam,Department of Mathematics

来源：

Positivity | 2017年 / 21卷

关键词：

cone-valued functions; locally convex cones; Korovkin type approximation; 46A03; 46A20; 46E10; 47B38; 47B60;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We consider ordered cones of continuous cone-valued functions on a locally compact Hausdorff space, endowed with appropriate locally convex topologies. Using suitable sets of such functions as test systems a Korovkin type approximation theorem for equicontinuous nets of positive operators is established. As in the classical theory, convergence is characterized both through envelopes for functions and through measure theoretical conditions.

引用

页码：449 / 472

页数：23

共 5 条

[1]

Bauer H(1978)Korovkin approximation in Math. Ann. 236 225-237

[2]

Donner K(1999)Bernstein-type approximation processes for vector-valued functions Acta Math. Hungar. 84 149-158

[3]

Nishishiraho T(2000)Hahn-Banach type theorems for locally convex cones J. Aust. Math. Soc. (Ser. A) 68 104-125

[4]

Roth W(2013)Korovkin theory for vector-valued functions on a locally compact space J. Approx. Theory 176 23-41

[5]

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