Positive linear relation and application to domination problem.

被引：0

作者：

Ayadi, Mohamed ^{[1
,2
]}

Baklouti, Hamadi ^{[2
]}

机构：

[1] Majmaah Univ, Coll Sci Al Zulfi, POB 66, Majmaah 11952, Saudi Arabia

[2] Sfax Univ, Fac Sci Sfax, Sfax, Tunisia

来源：

LINEAR & MULTILINEAR ALGEBRA | 2022年 / 70卷 / 19期

关键词：

Linear relation; positive operator; Riesz space; Banach lattice; PERTURBATION;

D O I：

10.1080/03081087.2020.1854166

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note we prove that positive multi-valued operators on Riesz spaces which are everywhere defined are always continuous. Further, we prove that the sum of two positive relations having the same null part is itself positive. This result allows us to study the domination problem in the class of positive relations.

引用

页码：3780 / 3789

页数：10

共 12 条

[1] POSITIVE COMPACT OPERATORS ON BANACH-LATTICES
ALIPRANTIS, CD
BURKINSHAW, O
[J]. MATHEMATISCHE ZEITSCHRIFT, 1980, 174 (03) : 289 - 298
[2] Alvarez T, 2012, PUBL MATH-DEBRECEN, V80, P155
[3] Positive linear relations between Riesz spaces
Ayadi, Mohamed
Baklouti, Hamadi
[J]. POSITIVITY, 2016, 20 (04) : 917 - 927
[4] Congruent spectrum for compact linear relations
Ayedi, Mohamed
Baklouti, Hamadi
[J]. PUBLICATIONES MATHEMATICAE-DEBRECEN, 2015, 87 (1-2): : 191 - 207
[5] Bahtin IA, 1962, SIB MAT ZH, V3
[6] Spectral theory of linear relations on real Banach spaces
Baskakov, A. G.
Zagorskii, A. S.
[J]. MATHEMATICAL NOTES, 2007, 81 (1-2) : 15 - 27
[7] Cross RW, 1998, MONOGRAPHS TXB PURE, V213
[8] Perturbation theory of lower semi-Browder multivalued linear operators
Fakhfakh, Fatma
Mnif, Maher
[J]. PUBLICATIONES MATHEMATICAE-DEBRECEN, 2011, 78 (3-4): : 595 - 606
[9] Meyer-Nieberg P., 1991, BANACH LATTICES
[10] Properties of Linear Relations in Banach Spaces
Ren, Guojing
Agarwal, Ravi P.
[J]. COMPLEX ANALYSIS AND OPERATOR THEORY, 2019, 13 (04) : 1917 - 1930

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