Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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GENERALIZED 𝛼-KÖTHE TOEPLITZ DUALS OF CERTAIN DIFFERENCE SEQUENCE SPACES

  • Sandeep Gupta (Department of Mathematics, Arya P.G. College) ;
  • Ritu (Department of Mathematics, Baba Mastnath University) ;
  • Manoj Kumar (Department of Mathematics, Baba Mastnath University)
  • Received : 2024.01.27
  • Accepted : 2024.04.16
  • Published : 2024.06.30
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Abstract

In this paper, we compute the generalized 𝛼-Köthe Toeplitz duals of the X-valued (Banach space) difference sequence spaces E(X, ∆), E(X, ∆𝜐) and obtain a generalization of the existing results for 𝛼-duals of the classical difference sequence spaces E(∆) and E(∆𝜐) of scalars, E ∈ {ℓ∞, c, c0}. Apart from this, we compute the generalized 𝛼-Köthe Toeplitz duals for E(X, ∆r) r ≥ 0 integer and observe that the results agree with corresponding results for scalar cases.

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Acknowledgement

We would like to thank the referee for helpful comments and suggestions, which improved the presentation of this paper.

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