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.
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.
Topological Algebras of Bounded Operators with Locally Solid Riesz Spaces
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.
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.
Aydın, A. (2018). Topological Algebras of Bounded Operators with Locally Solid Riesz Spaces. Erzincan University Journal of Science and Technology, 11(3), 543-549. https://doi.org/10.18185/erzifbed.413678