Regular vector lattices of continuous functions and Korovkin-type theorems - Part II

被引：8

作者：

Altomare, F ^{[1
]}

Cappelletti Montano, M ^{[1
]}

机构：

[1] Univ Bari, Dept Math, I-70125 Bari, Italy

来源：

STUDIA MATHEMATICA | 2006年 / 172卷 / 01期

关键词：

positive operator; positive projection; finitely defined operator; Korovkin-type approximation theorem; vector lattice of continuous functions;

D O I：

10.4064/sm172-1-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By applying the results of the first part of the paper, we establish some Korovkin-type theorems for continuous positive linear operators in the setting of regular vector lattices of continuous functions. Moreover, we present simple methods to construct Korovkin subspaces for finitely defined operators and for the identity operator and we determine those classes of operators which admit finite-dimensional Korovkin subspaces. Finally, we give a Korovkin-type theorem for continuous positive projections.

引用

页码：69 / 90

页数：22

共 18 条

[1] Regular vector lattices of continuous functions and Korovkin-type theorems - Part I [J].