Order compact and unbounded order compact operators on Riesz spaces

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Thesis Type: Postgraduate

Institution Of The Thesis: Hacettepe University, Fen Fakültesi, Matematik Bölümü, Turkey

Approval Date: 2020

Thesis Language: Turkish

Student: Şaziye Ece Özdemir

Supervisor: Nazife Erkurşun Özcan

Abstract:

Order convergence and unbounded order convergence are not topological terms in Riesz space. On the orher hand , compact operator takes an important place in functional analysis. In this thesis, we investigate order compact and unbounded order compact operators acting on Riesz spaces. An operator 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 uo-convergent subnet then it is called an unbounded order compact operator. 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.