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

https://izlik.org/JA44ZT58EH

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

https://izlik.org/JA44ZT58EH

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

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