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Journals / Hacettepe Journal of Mathematics and Statistics / 2010 / Cilt: 39 - Sayı: 3

On pairs of $ell$-Köthe spaces

Erdal KARAPINAR
Pages
337–349
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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

Deriving the characteristic $tilde{beta}$ from the characteristic $beta$, 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 $ell$ be a Banach sequence space with a monotone norm $parallel centerdot parallel_{ell}$, in which the canonical system ($e_i$) is a normalized unconditional basis.
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Key Findings & Data:We study the problem on isomorphic classification of pairs $F = biggl(K^{ell} biggl( exp biggl(-frac{1}{p}a_i biggr)biggr),K^{ell}biggl(exp biggl(-frac{1}{p}a_i + lambda_i biggr)biggr)biggr)$.
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Conclusion & Impact:Deriving the characteristic $tilde{beta}$ from the characteristic $beta$, 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:Domain Parameters

Abstract

Let $ell$ be a Banach sequence space with a monotone norm $parallel centerdot parallel_{ell}$, in which the canonical system ($e_i$) is a normalized unconditional basis. Let $a = (a_i), a_i rightarrow infty, lambda=(lambda_i)$ be sequences of positive numbers. We study the problem on isomorphic classification of pairs $F = biggl(K^{ell} biggl( exp biggl(-frac{1}{p}a_i biggr)biggr),K^{ell}biggl(exp biggl(-frac{1}{p}a_i + lambda_i biggr)biggr)biggr)$. For this purpose, we consider the sequence of so-called m-rectangle characteristics $mu^F_m$. It is shown that the system of all these characteristics is a complete quasidiagonal invariant on the class of pairs of finite-type $ell$-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 $tilde{beta}$ from the characteristic $beta$, 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

KARAPINAR, E. (2022). On pairs of $ell$-Köthe spaces. Hacettepe Journal of Mathematics and Statistics, Cilt: 39 - Sayı: 3, 337–349. https://ajindex.com/articles/529617

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