里兹空间和正交相加算子上的横向阶。二

IF 0.8 3区 数学 Q2 MATHEMATICS
Volodymyr Mykhaylyuk, Marat Pliev, Mikhail Popov
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引用次数: 0

摘要

本文旨在描述作者在前一篇论文中引入并研究的交集性质与其他已知的 Riesz 空间性质之间的关系,并证明 Riesz 空间的每个侧理想都是某个正交相加算子的内核(很容易看出每个正交相加算子的内核都是一个侧理想)。我们举例说明了具有主投影性质(因而也具有交集性质)的 Riesz 空间不具有 C-完备性。上述结果完整地回答了作者在本文第一部分提出的问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The lateral order on Riesz spaces and orthogonally additive operators. II

The present paper aims to describe the relationships between the intersection property, introduced and studied in the previous paper by the authors, with other known properties of Riesz spaces, and to prove that every lateral ideal of a Riesz space is a kernel of some positive orthogonally additive operator (it is easy to see that the kernel of every positive orthogonally additive operator is a lateral ideal). We provide examples of Riesz spaces with the principal projection property (and hence, with the intersection property) which fail to be C-complete. The above results give complete answers to problems posed in the first part of the present paper by the authors.

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来源期刊
Positivity
Positivity 数学-数学
CiteScore
1.80
自引率
10.00%
发文量
88
审稿时长
>12 weeks
期刊介绍: The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics and statistical decision theory are welcome. The scope of Positivity is to publish original papers in all areas of mathematics and its applications that are influenced by positivity concepts.
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