Topological Algebras of Bounded Operators with Locally Solid Riesz Spaces

Year 2018, Volume: 11 Issue: 3, 543 - 549, 30.12.2018

Abdullah Aydın

https://doi.org/10.18185/erzifbed.413678

Cited By: 1

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.

Keywords

Locally Solid Riesz Space, Operator, Order Bounded Operator, Vector Lattice

Topological Algebras of Bounded Operators with Locally Solid Riesz Spaces

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.

Keywords

Yerel Solid Riesz Uzayı, Operatör, Sıra Sınırlı Operatör, Kafes Uzayı

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.