On Compact Orthogonally Additive Operators

被引：0
作者：
Pliev, M. [1 ]
机构：
[1] Russian Acad Sci, Southern Math Inst, Vladikavkaz 362027, Russia
来源：
LOBACHEVSKII JOURNAL OF MATHEMATICS | 2021年 / 42卷 / 05期
基金：
俄罗斯基础研究基金会;
关键词：
orthogonally additive operator; AM-compact operator; positive operator; lateral projection; lateral band; C-complete vector lattice; Banach lattice; NARROW;
D O I：
10.1134/S1995080221050139
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article we explore orthogonally additive (nonlinear) operators in vector lattices. First we investigate the lateral order on vector lattices and show that with every element e of a C-complete vector lattice E is associated a lateral-to-order continuous orthogonally additive projection p(e) : E -> F-e. Then we prove that for an order bounded positive AM-compact orthogonally additive operator S : E -> F defined on a C-complete vector lattice E and taking values in a Dedekind complete vector lattice F all elements of the order interval [0, S] are AM-compact operators as well.
引用
收藏
页码：989 / 995
页数：7
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