As an application, we observethat the existence of an unbounded operator between ℓ -Köthe spaces, under a splitting condition, causes the existenceof a common basic subspace.
📌 3 Key Takeaways
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Objective & Hypothesis:Let ℓ be a Banach sequence space with a monotone norm in which the canonical system $(e_n)$ is anunconditional basis.
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Key Findings & Data:We show that if there exists a continuous linear unbounded operator between ℓ -Köthe spaces, thenthere exists a continuous unbounded quasidiagonal operator between them.
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Conclusion & Impact:As an application, we observethat the existence of an unbounded operator between ℓ -Köthe spaces, under a splitting condition, causes the existenceof a common basic subspace.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
Let ℓ be a Banach sequence space with a monotone norm in which the canonical system $(e_n)$ is anunconditional basis. We show that if there exists a continuous linear unbounded operator between ℓ -Köthe spaces, thenthere exists a continuous unbounded quasidiagonal operator between them. Using this result, we study the correspondingKöthe matrices when every continuous linear operator between ℓ -Köthe spaces is bounded. As an application, we observethat the existence of an unbounded operator between ℓ -Köthe spaces, under a splitting condition, causes the existenceof a common basic subspace.
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Cite This Article
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