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

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...

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Bibliographic Details
Published in:한국수학논문집, 32(4) 2024, 32(4), , pp.791-799
Main Authors: NAVEEN SHARMA, Sandeep Kumar(Department of Mathematics, D.A.V. College Muzaffarnagar, Chaudhary Charan Singh University, Meerut
Format: Article
Language:English
Subjects:
수학
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Summary: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. KCI Citation Count: 0
ISSN:1976-8605
2288-1433