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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 2

A note on topologically b-order bounded sets and generalized b-weakly compact operators

Nabil Machrafı(Mohammed V University)0000-0002-0667-6613
Birol Altın(GAZI UNIVERSITY)0000-0002-1085-809X
Pages
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Publication Date
2022-04-01
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AI Summary & Key Takeaways

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

We prove as a consequence that some well-known results on $b$-weakly compact operators on a Banach lattice extend in an improved version to generalized $b$-weakly compact operators on a Fréchet lattice.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We study the class of order weakly compact operators on locally solid Riesz spaces and the introduced class of generalized $b$-weakly compact operators on locally convex-solid Riesz spaces.
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Key Findings & Data:We study the class of order weakly compact operators on locally solid Riesz spaces and the introduced class of generalized $b$-weakly compact operators on locally convex-solid Riesz spaces.
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Conclusion & Impact:We prove as a consequence that some well-known results on $b$-weakly compact operators on a Banach lattice extend in an improved version to generalized $b$-weakly compact operators on a Fréchet lattice.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:b-order bounded set · order weakly compact operator · b-weakly compact operator

Abstract

We study the class of order weakly compact operators on locally solid Riesz spaces and the introduced class of generalized $b$-weakly compact operators on locally convex-solid Riesz spaces. We prove as a consequence that some well-known results on $b$-weakly compact operators on a Banach lattice extend in an improved version to generalized $b$-weakly compact operators on a Fréchet lattice.

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Cite This Article

Machrafı, N., Altın, B. (2022). A note on topologically b-order bounded sets and generalized b-weakly compact operators. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 2. https://doi.org/10.15672/hujms.961727

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