Unbounded asymptotic equivalences of operator nets with applications

被引：3

作者：

Erkursun-Ozcan, Nazife ^{[1
]}

Gezer, Niyazi Anil ^{[2
]}

机构：

[1] Hacettepe Univ, Dept Math, TR-06800 Ankara, Turkey

[2] Middle East Tech Univ, Dept Math, TR-06800 Ankara, Turkey

来源：

POSITIVITY | 2019年 / 23卷 / 04期

关键词：

Unbounded convergence; Asymptotic equivalence; Operator nets; ORDER CONVERGENCE; BEHAVIOR;

D O I：

10.1007/s11117-018-0640-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Present paper deals with applications of asymptotic equivalence relations on operator nets. These relations are defined via unbounded convergences on vector lattices. Given two convergences c and delta on a vector lattice, we study delta-asymptotic properties of operator nets formed by c-continuous operators. Asymptotic equivalences are known to be useful and extremely important tools to study infinite behaviors of strongly convergent operator nets and continuous semigroups. After giving a general theory, paper focuses on delta- martingale and delta-Lotz-Rabiger nets.

引用

页码：829 / 851

页数：23