Ideals and bands in pre-Riesz spaces

被引：0

作者：

Onno van Gaans

Anke Kalauch

机构：

[1] Leiden University,Mathematical Institute

[2] Institut für Analysis,undefined

[3] Fachrichtung Mathematik,undefined

[4] TU Dresden,undefined

来源：

Positivity | 2008年 / 12卷

关键词：

Band; disjointness; ideal; order dense subspace; partially ordered vector space; pre-Riesz space; solvex ideal; Primary 46A40; Secondary 06F20;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In a vector lattice, ideals and bands are well-investigated subjects. We study similar notions in a pre-Riesz space. The pre-Riesz spaces are exactly the order dense linear subspaces of vector lattices. Restriction and extension properties of ideals, solvex ideals and bands are investigated. Since every Archimedean directed partially ordered vector space is pre-Riesz, we establish properties of ideals and bands in such spaces.

引用

页码：591 / 611

页数：20