Kyungpook Mathematical Journal

  • 제63권2호
  • /
  • Pages.235-250
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  • 2023
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Duality of Paranormed Spaces of Matrices Defining Linear Operators from 𝑙p into 𝑙q

  • Kamonrat Kamjornkittikoon (Department of Mathematics and Statistics, Faculty of Science and Technology, Kanchanaburi Rajabhat University)
  • 투고 : 2022.11.17
  • 심사 : 2023.06.01
  • 발행 : 2023.06.30
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초록

Let 1 ≤ p, q < ∞ be fixed, and let R = [rjk] be an infinite scalar matrix such that 1 ≤ rjk < ∞ and supj,k rjk < ∞. Let 𝓑(𝑙p, 𝑙q) be the set of all bounded linear operator from 𝑙p into 𝑙q. For a fixed Banach algebra 𝐁 with identity, we define a new vector space SRp,q(𝐁) of infinite matrices over 𝐁 and a paranorm G on SRp,q(𝐁) as follows: let $$S^R_{p,q}({\mathbf{B}})=\{A:A^{[R]}{\in}{\mathcal{B}}(l_p,l_q)\}$$ and $G(A)={\parallel}A^{[R]}{\parallel}^{\frac{1}{M}}_{p,q}$, where $A^{[R]}=[{\parallel}a_{jk}{\parallel}^{r_{jk}}]$ and M = max{1, supj,k rjk}. The existance of SRp,q(𝐁) equipped with the paranorm G(·) including its completeness are studied. We also provide characterizations of β -dual of the paranormed space.

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과제정보

The author would like to thank Associate Professor Dr. Jitti-sak Rukbud of Silpakorn University in Thailand for reading this manuscript and providing insightful feedback. The author thanks the referees for several valuable suggestions and comments.

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