A NOTE ON NARROW OPERATORS ON COMPLEX RIESZ SPACES

被引：2
|
作者：
Popov, Mikhail [1 ,2 ]
机构：
[1] Pomeranian Univ Slupsk, Inst Exact & Tech Sci, Slupsk, Poland
[2] Vasyl Stefanyk Precarpathian Natl Univ, Ivano Frankivsk, Ukraine
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2024年 / 152卷 / 04期
关键词：
Complex Banach lattice; narrow operator; lateral order;
D O I：
10.1090/proc/16660
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The present paper continues investigation of narrow operators on complex vector lattices started in a recent paper by Dzhusoeva, Huang, Pliev and Sukochev. We answer their questions and strengthen one of their main results by proving that the extension TC: EC -+ FC of a linear operator T : E -+ F acting from a Dedekind complete real Riesz space E to a real Banach lattice F to their complexifications is narrow if and only if T is.
引用
收藏
页码：1703 / 1709
页数：7
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