Riesz Uzayları Üzerinde Tanımlı Sıra Kompakt ve Sınırsız Sıra Kompakt Operatörler

Abstract

Order convergence and unbounded order convergence are not topological terms on Riesz space. On the other hand, compact operatör takes an important place in functional analysis. In this thesis, we investigate order compact and unbounded order compact operators acting on Riesz spaces. An operatör is said to be order compact if it maps an arbitrary order bounded net to a net with an order convergent subnet. In the same way, if an operator maps order bounded net to a net with unbounded order convergent subnet then it is called an unbounded order compact operatör. We expose the relationships between order compact, unbounded order compact, semi-compact and GAM-compact operators. Since order convergence and unbounded order convergence are not topological, we derive new results related to these classes of operators. The results are included in the article [10] in the bibliography section.