uτ-convergence in locally solid vector lattices

被引：0

作者：

Dabboorasad, Y. A. ^{[1
,2
]}

Emelyanov, E. Y. ^{[2
]}

Marabeh, M. A. A. ^{[3
]}

机构：

[1] Islamic Univ Gaza, Dept Math, POB 108, Gaza City, Palestine

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

[3] Palestine Tech Univ Kadoorie, Coll Sci & Arts, Dept Appl Math, Tulkarem, Palestine

来源：

POSITIVITY | 2018年 / 22卷 / 04期

关键词：

Banach lattice; Vector lattice; ut-convergence; ut-topology; uo-convergence; un-convergence; un-topology; UNBOUNDED ORDER CONVERGENCE; BANACH-LATTICES;

D O I：

10.1007/s11117-018-0559-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let be a net in a locally solid vector lattice ; we say that is unbounded -convergent to a vector if for all . In this paper, we study general properties of unbounded -convergence (shortly -convergence). -convergence generalizes unbounded norm convergence and unbounded absolute weak convergence in normed lattices that have been investigated recently. We introduce -topology and briefly study metrizability and completeness of this topology.

引用

页码：1065 / 1080

页数：16

共 29 条

[1] Abramovich Y. A., 2002, Graduate Studies in Mathematics
[2] Aliprantis C.D., 2003, Mathematical Surveys and Monographs, V105
[3] Aliprantis C. D., 2006, POSITIVE OPERATORS
[4] [Anonymous], [No title captured]
[5] Compact-like operators in lattice-nonmed. spaces
Aydin, A.
Emelyanov, E. Yu.
Ozcan, N. Erkursun
Marabeh, M. A. A.
[J]. INDAGATIONES MATHEMATICAE-NEW SERIES, 2018, 29 (02): : 633 - 656
[6] Aydin A., ARXIV160905301V3
[7] Dabboorasad Y., ARXIV170509883V1
[8] Unbounded norm convergence in Banach lattices
Deng, Y.
O'Brien, M.
Troitsky, V. G.
[J]. POSITIVITY, 2017, 21 (03) : 963 - 974
[9] [Емельянов Э.Ю. Emelyanov Eduard Yu.], 2016, [Владикавказский математический журнал, Vladikavkazskii matematicheskii zhurnal], V18, P21
[10] Engelking R., 1989, General Topology

← 1 2 3 →