A short note on band projections in partially ordered vector spaces

被引：3
作者：
Glueck, Jochen
机构：
来源：
INDAGATIONES MATHEMATICAE-NEW SERIES | 2019年 / 30卷 / 01期
关键词：
Band projection; Order projection; Pre-Riesz space; Partially ordered vector space; Disjointness; DISJOINTNESS;
D O I：
10.1016/j.indag.2018.09.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Consider an Archimedean partially ordered vector space X with generating cone (or, more generally, a pre-Riesz space X). Let P be a linear projection on X such that both P and its complementary projection I - P are positive; we prove that the range of P is a band. This shows that the well-known concept of band projections on vector lattices can, to a certain extent, be transferred to the framework of ordered vector spaces. (C) 2018 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：1 / 6
页数：6
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