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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 39 Issue: 3

On Pairs of l-Köthe Spaces

Erdal Karapınar
Pages
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Publication Date
2010-03-01
DOI
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AI Summary & Key Takeaways

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

Deriving the characteristic βe from the characteristic β, and using the interpolation method of analytic scale, we are able to generalize some results of Chalov, Dragilev, and Zahariuta (Pair of finite type power series spaces, Note di Mathematica 17, 121–142, 1997).

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let ℓ be a Banach sequence space with a monotone norm k · kℓ, in which the canonical system (ei) is a normalized unconditional basis.
📊
Key Findings & Data:We study the problem on isomorphic classification of pairs F = K ℓ exp − 1 p ai , Kℓ exp − 1 p ai + λi .
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Conclusion & Impact:Deriving the characteristic βe from the characteristic β, and using the interpolation method of analytic scale, we are able to generalize some results of Chalov, Dragilev, and Zahariuta (Pair of finite type power series spaces, Note di Mathematica 17, 121–142, 1997).
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:m-rectangular characteristic · Power ℓ-K¨othe spaces · Linear topological invariants

Abstract

Let ℓ be a Banach sequence space with a monotone norm k · kℓ, in which the canonical system (ei) is a normalized unconditional basis. Let a = (ai), ai → ∞, λ = (λi) be sequences of positive numbers. We study the problem on isomorphic classification of pairs F = K ℓ exp − 1 p ai , Kℓ exp − 1 p ai + λi . For this purpose, we consider the sequence of so-called m-rectangle characteristics µ F m. It is shown that the system of all these characteristics is a complete quasidiagonal invariant on the class of pairs of finite-type ℓ-power series spaces. By using analytic scale and a modification of some invariants (modified compound invariants) it is proven that m-rectangular characteristics are invariant on the class of such pairs. Deriving the characteristic βe from the characteristic β, and using the interpolation method of analytic scale, we are able to generalize some results of Chalov, Dragilev, and Zahariuta (Pair of finite type power series spaces, Note di Mathematica 17, 121–142, 1997).

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Cite This Article

Karapınar, E. (2010). On Pairs of l-Köthe Spaces. Hacettepe Journal of Mathematics and Statistics, Volume: 39 Issue: 3. https://ajindex.com/articles/1403699

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