Research Article
Year 2018,
Volume: 11 Issue: 3, 543 - 549, 30.12.2018
Abstract
Suppose is a vector lattice
and is a locally solid
vector lattice. An operator is said to be -bounded if, for every order bounded set is topological bounded
in . In this paper, we study on algebraic properties of -bounded operators with the equicontinuous convergence
topology and uniform convergence topology.
References
- Aliprantis, C.D., Burkinshaw, O. 2003. Locally Solid Riesz Spaces with Applications to Economics 2nd ed., American Mathematical Society, United States.
- Aliprantis, C.D., Burkinshaw, O. 2006. Positive Operators, Springer Netherlands, London.
- Aydın, A., Gorokhova S.G., Gül, H. 2018. Nonstandard Hulls of Lattice-Normed Ordered Vector Spaces, Turkish Journal of Mathematics, 42(1), 155 – 163.
- Aydın, A., Emel'yanov E., Erkurşun N.Ö., Marabeh, M.A.A. 2018. Compact-Like Operators in Lattice-Normed Spaces, Indagationes Mathematicae, 29(1), 633-656.
- Hong, L. 2016. On Order Bounded Subsets of Locally Solid Riesz Spaces, Quaestiones Mathematicae, 39(3), 381-389.
- Troitsky, V.G. 2004. Measures of Non-Compactness of Operators on Banach Lattices, Positivity, 8(2), 165–178.
- Zabeti, O. 2017. Topological Algebras of Locally Solid Vector Subspaces of Order Bounded Operators, Positivity, 21(4), 1253–1259.
Year 2018,
Volume: 11 Issue: 3, 543 - 549, 30.12.2018
Abstract
bir kafes uzayı ve de bir yerel solid kafes uzayı olsun. Eğer 'deki her sıra sınırlıalt kümesi için, 'de topolojik olarak sınırlı oluyorsa; operatörüne -sınırlı operatör denir. Bu çalışmamızda, -sınırlılığın cebirsel özelliklerini denk-süreklilik
yakınsamasındaki ve düzgün yakınsamasındaki topolojilere göre inceledik.
yakınsamasındaki ve düzgün yakınsamasındaki topolojilere göre inceledik.
References
- Aliprantis, C.D., Burkinshaw, O. 2003. Locally Solid Riesz Spaces with Applications to Economics 2nd ed., American Mathematical Society, United States.
- Aliprantis, C.D., Burkinshaw, O. 2006. Positive Operators, Springer Netherlands, London.
- Aydın, A., Gorokhova S.G., Gül, H. 2018. Nonstandard Hulls of Lattice-Normed Ordered Vector Spaces, Turkish Journal of Mathematics, 42(1), 155 – 163.
- Aydın, A., Emel'yanov E., Erkurşun N.Ö., Marabeh, M.A.A. 2018. Compact-Like Operators in Lattice-Normed Spaces, Indagationes Mathematicae, 29(1), 633-656.
- Hong, L. 2016. On Order Bounded Subsets of Locally Solid Riesz Spaces, Quaestiones Mathematicae, 39(3), 381-389.
- Troitsky, V.G. 2004. Measures of Non-Compactness of Operators on Banach Lattices, Positivity, 8(2), 165–178.
- Zabeti, O. 2017. Topological Algebras of Locally Solid Vector Subspaces of Order Bounded Operators, Positivity, 21(4), 1253–1259.
There are 7 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | December 30, 2018 |
| Published in Issue | Year 2018 Volume: 11 Issue: 3 |