In this paper a) we describe all S-bounded subsets of $varphi$ ; b) we precisely characterize the matrix transformations from X into Y which are continuous with respect to strong $varphi$-topologies on X and Y.
📌 3 Key Takeaways
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Objective & Hypothesis:Let S be the vector space of all complex sequences, X and Y be any two subspaces of S and $varphi$ be the vector space of sequences which have only a finite number of non-zero terms.
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Key Findings & Data:Let S be the vector space of all complex sequences, X and Y be any two subspaces of S and $varphi$ be the vector space of sequences which have only a finite number of non-zero terms.
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Conclusion & Impact:In this paper a) we describe all S-bounded subsets of $varphi$ ; b) we precisely characterize the matrix transformations from X into Y which are continuous with respect to strong $varphi$-topologies on X and Y.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
Let S be the vector space of all complex sequences, X and Y be any two subspaces of S and $varphi$ be the vector space of sequences which have only a finite number of non-zero terms. In this paper a) we describe all S-bounded subsets of $varphi$ ; b) we precisely characterize the matrix transformations from X into Y which are continuous with respect to strong $varphi$-topologies on X and Y.
Özet
S bütün kompleks dizilerin uzayı, X ve Y, S nin iki alt vektör uzayı ve $varphi$ de S deki sonlu dizilerin alt uzayı olsun. Bu makalede a) $varphi$ nin bütün S- sınırlı kümeleri belirlenmiştir, b) Güçlü $varphi$- topolojisine göre X den Y ye sürekli olan bütün matrisler karakterize edilmiştir.
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Cite This Article
ARGÜN, Z. (2022). Dizi uzayları üzerinde güçlü $phi$ topolojisine göre sürekli matris dönüşümleri. Gazi Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 13 - Sayı: 4, 1129–1135. https://ajindex.com/articles/522472
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