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.

Anahtar Kelimeler:

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

Topological Algebras of Bounded Operators with Locally Solid Riesz Spaces

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,

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