Topological Algebras of Bounded Operators with Locally Solid Riesz Spaces

Öz

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.

Anahtar Kelimeler

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

Topological Algebras of Bounded Operators with Locally Solid Riesz Spaces

Öz

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.

Anahtar Kelimeler

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

Kaynakça

1. Aliprantis, C.D., Burkinshaw, O. 2003. Locally Solid Riesz Spaces with Applications to Economics 2nd ed., American Mathematical Society, United States.
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7. Zabeti, O. 2017. Topological Algebras of Locally Solid Vector Subspaces of Order Bounded Operators, Positivity, 21(4), 1253–1259.