Korean J. Math. Vol. 32 No. 4 (2024) pp.791-799
DOI: https://doi.org/10.11568/kjm.2024.32.4.791

Generalized $\eta$-duals of Banach space valued difference sequence spaces

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Published: Dec 30, 2024
Keywords:
Difference sequence spaces, Köthe Toeplitz duals, Generalized Köthe Toeplitz duals
Mathematics Subject Classification:
46A45, 40A05

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Sandeep Kumar
Department of Mathematics, D.A.V. College Muzaffarnagar, Chaudhary Charan Singh University, Meerut (India)
Naveen Sharma
Department of Mathematics, D.A.V. College Muzaffarnagar, Chaudhary Charan Singh University, Meerut (India)

Abstract

In the present paper, we get an opportunity to introduce and study the notion of generalized $\eta$-dual for Banach space valued difference sequence spaces, as a generalization of the classical $\alpha$-Köthe Toeplitz dual for scalar sequences. We obtain a set of necessary and sufficient conditions for $(A_k)\in E^\eta(X, \Delta) $, where $E \in \{ \ell_\infty,\,c,\,c_0 \}$. Moreover, we explore the notion of generalized $\eta$-dual for generalized difference sequence spaces $ E(X,\Delta^r)$ and $E(X,\Delta_\nu)$, where $r\in\mathbb{N}$ and $\nu$ is a multiplier sequence.


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