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Journals / Turkish Journal of Mathematics / 2021 / Cilt: 45 - Sayı: 2

Order compact and unbounded order compact operators

Niyazi Anıl GEZER
Şaziye Ece ÖZDEMİR
İrem Mesude URGANCI
Nazife ERKURŞUN ÖZCAN
Pages
634–646
Publication Date
2022-11-04
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

By using the nontopologicalconcepts of order and unbounded order convergences, we derive new results related to these classes of operators.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We investigate properties of order compact, unbounded order compact and relatively uniformly compactoperators acting on vector lattices.
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Key Findings & Data:An operator is said to be order compact if it maps an arbitrary order bounded netto a net with an order convergent subnet.
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Conclusion & Impact:By using the nontopologicalconcepts of order and unbounded order convergences, we derive new results related to these classes of operators.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

We investigate properties of order compact, unbounded order compact and relatively uniformly compactoperators acting on vector lattices. An operator is said to be order compact if it maps an arbitrary order bounded netto a net with an order convergent subnet. Analogously, an operator is said to be unbounded order compact if it mapsan arbitrary order bounded net to a net with uo-convergent subnet. After exposing the relationships between ordercompact, unbounded order compact, semicompact and GAM -compact operators; we study those operators mappingan arbitrary order bounded net to a net with a relatively uniformly convergent subnet. By using the nontopologicalconcepts of order and unbounded order convergences, we derive new results related to these classes of operators.

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Cite This Article

GEZER, N. A., ÖZDEMİR, Ş. E., URGANCI, İ. M., ÖZCAN, N. E. (2022). Order compact and unbounded order compact operators. Turkish Journal of Mathematics, Cilt: 45 - Sayı: 2, 634–646. https://ajindex.com/articles/607470

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