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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Many examples are given to illustrate the essential conditions.
📌 3 Key Takeaways
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Objective & Hypothesis:In the present article, we expose various properties of unbounded absolutely weak Dunford?Pettis and unbounded absolutely weak compact operators on a Banach lattice E.
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Key Findings & Data:In addition to their topological and lattice properties, we investigate relationships between M-weakly compact operators, L-weakly compact operators, and order weakly compact operators with unbounded absolutely weak Dunford-Pettis operators.
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Conclusion & Impact:Many examples are given to illustrate the essential conditions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:uaw-Convergence · uaw-Dunford-Pettis operator · Banach lattice
Abstract
In the present article, we expose various properties of unbounded absolutely weak Dunford?Pettis and unbounded absolutely weak compact operators on a Banach lattice E. In addition to their topological and lattice properties, we investigate relationships between M-weakly compact operators, L-weakly compact operators, and order weakly compact operators with unbounded absolutely weak Dunford-Pettis operators. We show that the square of any positive uaw-Dunford-Pettis (M-weakly compact) operator on an order continuous Banach lattice is compact. Many examples are given to illustrate the essential conditions.
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Cite This Article
ÖZCAN, N. E., GEZER, N. A., ZABETI, O. (2019). Unbounded absolutely weak Dunford-Pettis operators. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 6, 2731–2740. https://ajindex.com/articles/198149